# How do you solve the equation abs(ax)=b?

Aug 9, 2017

Assuming the solution being requested is for $x$, see a solution process below:

#### Explanation:

The absolute value function takes any negative or positive term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1

$a x = - b$

$\frac{a x}{\textcolor{red}{a}} = - \frac{b}{\textcolor{red}{a}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{a}}} x}{\cancel{\textcolor{red}{a}}} = - \frac{b}{a}$

$x = - \frac{b}{a}$

Solution 2

$a x = b$

$\frac{a x}{\textcolor{red}{a}} = \frac{b}{\textcolor{red}{a}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{a}}} x}{\cancel{\textcolor{red}{a}}} = \frac{b}{a}$

$x = \frac{b}{a}$

The Solutions Are: $x = - \frac{b}{a}$ and $x = \frac{b}{a}$