# How do you solve |-5x + -2| + 3 = 11?

Jan 26, 2017

$x = - 2 \text{ or } x = \frac{6}{5}$

#### Explanation:

Equations involving the $\textcolor{b l u e}{\text{absolute value}}$ have 2 solutions.

Isolate the absolute value, noting that

$- 5 x + - 2 = - 5 x - 2$

subtract 3 from both sides.

$| - 5 x - 2 | \cancel{+ 3} \cancel{- 3} = 11 - 3$

$\Rightarrow | - 5 x - 2 | = 8$

The 2 solutions are obtained by solving $- 5 x - 2 = \textcolor{red}{\pm} 8$

$\textcolor{b l u e}{\text{Solution 1}}$

$- 5 x - 2 = 8$

$- 5 x \cancel{- 2} \cancel{+ 2} = 8 + 2$

$\Rightarrow - 5 x = 10 \Rightarrow x = \frac{10}{- 5} = - 2$

$\textcolor{b l u e}{\text{Solution 2}}$

$- 5 x - 2 = - 8$

$- 5 x = - 8 + 2$

$\Rightarrow - 5 x = - 6 \Rightarrow x = \frac{- 6}{- 5} = \frac{6}{5}$

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

"left side "=|(-5xx-2)-2|+3=|8|+3=8+3=11 ✔︎

$\text{left side } = | \left(- {\cancel{5}}^{1} \times \frac{6}{\cancel{5}} ^ 1\right) - 2 | + 3$

=|-6-2|+3=|-8|+3=8+3=11 ✔︎