MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8DB7A.C1782A30" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/master06.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Click to edit Master title style<= /div>
Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
‹date/time›
‹footer›
‹#›
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADwQAAAAUAHAAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAAC8AgAAAAAAQAAiQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACGAAAADIKNABwAQsAAABFeHByZXNzaW9ucwAdABgAHAAR ABkAGQAYAAwAGwAcABgABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAA AAAYAAAALJ4TAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwADAAAAAAA= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0183.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5<= /span>
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0184.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0185.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0186.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For= the x-term ax, the number “a” is called the coefficient of the term.
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0187.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For= the x-term ax, the number “a” is called the coefficient of the term. When we multiply a nu= mber to an x-term, we multiply it to the coefficient.
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0188.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For= the x-term ax, the number “a” is called the coefficient of the term. When we multiply a nu= mber to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0189.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For the x-term ax, the number “a” is called the coefficient of the term. When we multiply a number to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
and –2(–4x) =3D (–2)(–4)x =3D 8x.
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0190.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For the x-term ax, the number “a” is called the coefficient of the term. When we multiply a number to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
and –2(–4x) =3D (–2)(–4)x =3D 8x.
We may multiply a number to an expression and expand the result by the distributive law.=
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0191.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For the x-term ax, the number “a” is called the coefficient of the term. When we multiply a number to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
and –2(–4x) =3D (–2)(–4)x =3D 8x.
We may multiply a number to an expression and expand the result by the distributive law.
Distributive Law:
A(B ± C) =3D AB &pl= usmn; AC =3D (B ± C)A
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0192.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For the x-term ax, the number “a” is called the coefficient of the term. When we multiply a number to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
and –2(–4x) =3D (–2)(–4)x =3D 8x.
We may multiply a number to an expression and expand the result by the distributive law.
Distributive Law:
A(B ± C) =3D AB &pl= usmn; AC =3D (B ± C)A
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
Example B. Expand then simplify
=
a.  –5(2x – 4)
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0193.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For the x-term ax, the number “a” is called the coefficient of the term. When we multiply a number to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
and –2(–4x) =3D (–2)(–4)x =3D 8x.
We may multiply a number to an expression and expand the result by the distributive law.
Distributive Law:
A(B ± C) =3D AB &pl= usmn; AC =3D (B ± C)A
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
Example B. Expand then simplify
=
a.  –5(2x – 4)
=3D –5(2x) – (–5)(4)
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0194.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
For the x-term ax, the number “a” is called the coefficient of the term. When we multiply a number to an x-term, we multiply it to the coefficient. Hence, 3(5x) =3D (3*5)x =3D15x, 
and –2(–4x) =3D (–2)(–4)x =3D 8x.
We may multiply a number to an expression and expand the result by the distributive law.
Distributive Law:
A(B ± C) =3D AB &pl= usmn; AC =3D (B ± C)A
Expressions
Example A. Combine
=
   2x – 4 + 9 – 5x=
=3D 2x – 5x – 4 + 9
=3D –3x + 5=  
Example B. Expand then simplify
=
a.  –5(2x – 4)
=3D –5(2x) – (–5)(4)
=3D –10x + 20  
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0155.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0195.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0195_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0196.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12   
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0196_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0196_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0197.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8    
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0197_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0197_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0197_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0198.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0198_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0198_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0198_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0198_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0199.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0199_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0199_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0199_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0199_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0200.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0200_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0200_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0200_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0200_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0201.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x  
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0201_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0201_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0201_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0201_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0201_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15     
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0202_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x 
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0203_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
Expressions
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0204_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0205_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
( but not as        = ;  )
p
qx
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image057.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0206_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
( but not as        = ;  ) since
p
qx
p
q
x =3D
p
q
x
1
  =3D
px
q
*
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image078.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image079.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0207_image080.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
( but not as        = ;  ) since
p
qx
p
q
x =3D
p
q
x
1
  =3D
px
q
Hence        = ;  is the same as        .     <= /span>
2x
3
2
3
x
*
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image081.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image082.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image083.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image084.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image085.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image086.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image087.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image088.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image089.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image090.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image092.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image093.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image094.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image095.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image096.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0208_image097.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
( but not as        = ;  ) since
p
qx
p
q
x =3D
p
q
x
1
  =3D
px
q
Example C.  Evaluate        = ;  if x =3D 6.
4
3
x
Hence        = ;  is the same as        .     <= /span>
2x
3
2
3
x
*
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image098.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image099.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image100.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image101.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image102.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image103.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image104.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image105.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image106.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image107.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image108.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image109.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image110.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image111.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image112.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image113.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image114.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0209_image115.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
( but not as        = ;  ) since
p
qx
p
q
x =3D
p
q
x
1
  =3D
px
q
Example C.  Evaluate        = ;  if x =3D 6.
4
3
x
Set x =3D (= 6) in
Hence        = ;  is the same as        .     <= /span>
2x
3
2
3
x
*
4
3
x, <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:#006600;mso-fareast-language:ZH-CN;mso-special-= format: lastCR;display:none'>
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image116.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image117.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image118.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image119.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image120.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image121.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image122.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image123.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image124.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image125.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image126.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image127.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image128.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image129.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image130.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image131.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image132.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image133.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0210_image134.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or
px
q
( but not as        = ;  ) since
p
qx
p
q
x =3D
p
q
x
1
  =3D
px
q
Example C.  Evaluate        = ;  if x =3D 6.
4
3
x
we get
Set x =3D (= 6) in
4
3
Hence        = ;  is the same as        .     <= /span>
2x
3
2
3
x
*
4
3
x, <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:#006600;mso-fareast-language:ZH-CN;mso-special-= format: lastCR;display:none'>
(6) =
------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image135.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image136.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image137.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIXBGKJedy8lIuGPgmnzhyfAIKfOEZktRQAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image138.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image139.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image140.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAF ABUAgAAAAAAAAAIUBGKGuZr3GmSx0uvwzKH344HNlxUAOx== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image141.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAG ABUAgAAAAAAAAAIYBBJmqJfK4FvTtUhvxVbq7zkIMz5lmAEFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image142.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAF ABYAgAAAAAAAAAIVBGKGuZr3GmSx0uvwzKH7f3SKmGUFADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image143.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image144.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image145.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image146.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image147.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image148.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image149.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image150.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image151.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image152.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image153.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0211_image154.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C8DB7A.C1782A30 Content-Location: file:///C:/2D664A33/1Expressions_files/slide0212.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Expressions
b.  3(2x – 4) + 2(4 – 5x)=
 
    =3D 6x – 12    + 8 – 10x <= /span>
    =3D –4x –= 4
 
c. –3(̵= 1; 3x + 5) – 2(– 4x – 6)
 
    =3D  9x    – 15      + 8x  + 12
    =3D  17x – 3
Expressions
X-terms with fractional coefficients may be written in two ways:
p
q
x or