# How do you solve the equation abs(5-6x)=7?

May 30, 2017

$x = - \frac{1}{3} \text{ or } x = 2$

#### Explanation:

$\text{the expression inside the absolute value can be positive or}$
$\text{negative}$

$\Rightarrow 5 - 6 x = \textcolor{red}{\pm} 7$

$\textcolor{b l u e}{\text{first solution}}$

$5 - 6 x = \textcolor{red}{+} 7$

$\text{subtract 5 from both sides}$

$\Rightarrow - 6 x = 2$

$\text{divide both sides by - 6}$

$\Rightarrow x = \frac{2}{- 6} = - \frac{1}{3}$

$\textcolor{b l u e}{\text{second solution}}$

$5 - 6 x = \textcolor{red}{-} 7$

$\text{subtract 5 from both sides}$

$\Rightarrow - 6 x = - 12$

$\text{divide both sides by - 6}$

$\Rightarrow x = \frac{- 12}{- 6} = 2$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

$x = - \frac{1}{3} \to | 5 + 2 | = | 7 | = 7$

$x = 2 \to | 5 - 12 | = | - 7 | = 7$

$\Rightarrow x = - \frac{1}{3} \text{ or "x=2" are the solutions}$