# How do you graph and solve |2x-6|>|x+4|?

Feb 8, 2017

$x < \frac{2}{3} \textcolor{w h i t e}{\text{XX")orcolor(white)("XX}} x > 10$

(graphed as a number line)

#### Explanation:

If $\left\mid 2 x - 6 \right\mid > \left\mid x + 4 \right\mid$
then
$\textcolor{w h i t e}{\text{XXX}} {\left(2 x - 6\right)}^{2} > {\left(x + 4\right)}^{2}$

$\textcolor{w h i t e}{\text{XXX}} 4 {x}^{2} - 24 x + 36 > {x}^{2} + 8 x + 16$

$\textcolor{w h i t e}{\text{XXX}} 3 {x}^{2} - 32 x + 20 > 0$

$\textcolor{w h i t e}{\text{XXX}} \left(3 x - 2\right) \left(x - 10\right) > 0$

This can only be true if:
[1] both factors are greater than $0$
color(white)("XXX")"if " x > 2/3 " "underline("and")" " x > 10rarr x > 10
or
[2] both factors are less than $0$
color(white)("XXX")"if " x < 2/3 " "underline("and")" " x < 10 rarr x <2/3