# How do you solve - 5| x + 1| = -10?

Nov 24, 2017

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

#### Explanation:

$\text{divide both sides by } - 5$

$\frac{\cancel{- 5}}{\cancel{- 5}} | x + 1 | = \frac{- 10}{- 5}$

$\Rightarrow | x + 1 | = 2$

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

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

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

$x + 1 = 2 \Rightarrow x = 2 - 1 = 1$

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

$- \left(x + 1\right) = 2$

$\Rightarrow - x - 1 = 2$

$\Rightarrow - x = 2 + 1 = 3 \Rightarrow x = - 3$

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

$x = 1 \to - 5 | 2 | = - 5 \times 2 = - 10 \leftarrow \text{True}$

$x = - 3 \to - 5 | - 3 + 1 | = - 5 | - 2 \models - 10 \leftarrow \text{True}$