# How do you solve abs(5-2x)=13?

Mar 2, 2018

$x = - 4 \text{ or } x = 9$

#### Explanation:

$\text{the value inside the "color(blue)"absolute value bars "" can be}$
$\text{positive or negative }$

$\Rightarrow \text{there are 2 possible solutions}$

$5 - 2 x = 13 \leftarrow \textcolor{red}{\text{positive inside bars}}$

$\text{subtract 5 from both sides}$

$\cancel{5} \cancel{- 5} - 2 x = 13 - 5$

$\Rightarrow - 2 x = 8$

$\text{divide both sides by } - 2$

$\frac{\cancel{- 2} x}{\cancel{- 2}} = \frac{8}{- 2}$

$\Rightarrow x = - 4 \leftarrow \textcolor{b l u e}{\text{first solution}}$

$- \left(5 - 2 x\right) = 13 \leftarrow \textcolor{red}{\text{negative inside bars}}$

$\Rightarrow - 5 + 2 x = 13$

$\text{add 5 to both sides}$

$\cancel{- 5} \cancel{+ 5} + 2 x = 13 + 5$

$\Rightarrow 2 x = 18$

$\text{divide both sides by 2}$

$\frac{\cancel{2} x}{\cancel{2}} = \frac{18}{2}$

$\Rightarrow x = 9 \leftarrow \textcolor{b l u e}{\text{second solution}}$

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

$\text{Substitute these 2 possible solutions into the left side}$
$\text{of the equation and if equal to right side then they are}$
$\text{the solutions}$

$x = - 4 \Rightarrow | 5 + 8 | = | 13 | = 13 \leftarrow \text{ True}$

$x = 9 \Rightarrow | 5 - 18 | = | = 13 | = 13 \leftarrow \text{ True}$

$\Rightarrow x = - 4 \text{ or "x=9" are the solutions}$