# How do you solve -63= - 9| w |?

May 9, 2018

$\textcolor{b l u e}{w = \pm 7}$

#### Explanation:

$- 63 = - 9 | w |$

First divide both sides by $- 9$

$| w | = 7$

By the definition of absolute value:

$| a | = a \textcolor{w h i t e}{8888.8} \boldsymbol{\text{if and only if}} \textcolor{w h i t e}{888} a \ge 0$

$| a | = - a \textcolor{w h i t e}{888} \boldsymbol{\text{if and only if}} \textcolor{w h i t e}{888} a < 0$

Because of this we need to solve both:

$w = 7$

and

$- \left(w\right) = 7$

$\therefore$

$w = 7 \mathmr{and} w = - 7$

$w = \pm 7$