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 February 17th, 2013, 01:25 PM #1 Member   Joined: Feb 2013 Posts: 44 Thanks: 0 I need help with this homework question x-8 ---- less than or equal to 2 x-4
 February 17th, 2013, 01:29 PM #2 Member   Joined: Feb 2013 Posts: 44 Thanks: 0 Re: i need help with this homework question Just to clarify, that's x-8 DIVIDED by x-4.
February 17th, 2013, 02:52 PM   #3
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Re: I need help with this homework question

Hello, hamburgertime!

Quote:
 $\frac{ x\,-\,8}{x\,-\,4} \:\le \:2$

$\text{W\!e have: }\:\frac{x\,-\,8}{x\,-\,4} \,-\,2 \:\le\:0 \;\;\;\Rightarrow\;\;\;\frac{(x\,-\, \,-\,2(x\,-\,4)}{x\,-\,4} \:\le\:0" />

[color=beige]. . . . . . . [/color]$\frac{x\,-\,8\,-\,2x\,+\,8}{x\,-\,4}\:\le\:0 \;\;\;\Rightarrow\;\;\; \frac{-x}{x\,-\,4}\:\le\:0 \;\;\;\Rightarrow\;\;\; \frac{x}{x\,-\,4} \:\ge\:0 \;\;\;$

$\text{A fraction is positive if the numerator and denominator have the same sign.}$

$\text{Both positive: }\:\begin{Bmatrix}x \:\ge\:0 \\ \\ \\ x\,-\,4\:\ge\:0 \;\;\; \Rightarrow \;\;\; x \:\ge\:4 \end{Bmatrix}\;\;\;\Rightarrow \;\;\; x \:\ge\:4$

$\text{Both negative: }\:\begin{Bmatrix} x \:\le\:0 \\ \\ \\ x\,-\,4\:\le\:0 \;\;\;\Rightarrow\;\;\; x \:\le\:4 \end{Bmatrix} \;\;\;\Rightarrow\;\;\;x \:\le\:0$

$\text{Therefore: }\-\infty,\,0) \,\cup\,(4,\,\infty)" />

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