# How do you solve |x + 5| = 9?

Apr 22, 2018

The solutions are $S = \left\{4 , - 14\right\}$

#### Explanation:

To solve equation with absolute values, procced as follows :

$\left\{\left(| x + 5 | = 9\right) :\right\}$

$\iff$, $\left\{\begin{matrix}x + 5 = 9 \\ - x - 5 = 9\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x = 9 - 5 \\ x = - 5 - 9\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x = 4 \\ x = - 14\end{matrix}\right.$

The solutions are $S = \left\{4 , - 14\right\}$

graph{|x+5|-9 [-19.56, 12.48, -7.99, 8.03]}

Apr 22, 2018

$x = - 14 \text{ or } x = 4$

#### Explanation:

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

$\textcolor{m a \ge n t a}{\text{Positive value}}$

$x + 5 = 9 \Rightarrow x = 9 - 5 = 4$

$\textcolor{m a \ge n t a}{\text{Negative value}}$

$- \left(x + 5\right) = 9$

$\Rightarrow - x - 5 = 9 \Rightarrow - x = 9 + 5 = 14 \Rightarrow x = - 14$

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

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

$x = 4 \Rightarrow | 4 + 5 | = | 9 | = 9$

$x = - 14 \Rightarrow | - 14 + 5 | = | - 9 | = 9$

$\Rightarrow x = - 14 \text{ or "x=4" are the silutions}$