# How do you solve |-5x + -2| = 12?

Aug 1, 2016

$x = - \frac{14}{5}$ and $x = 2$

#### Explanation:

We are given $\left\mid - 5 x + - 2 \right\mid = 12$. To solve this, we should first simplify the expression inside the absolute value bars, like this $- 5 x - 2$. Okay... that's pretty much it. Now we move on to the next step.

Absolute value bars make whatever is within them positive. That means that we need to find two vaues for $x$: one positive and one negative.

So, instead of one equation, we have two. $\left\mid - 5 x - 2 \right\mid = 12$ becomes $- 5 x - 2 = 12$ and $- 5 x - 2 = - 12$. Now we just solve for $x$.

$- 5 x - 2 = 12$ $\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .}$ $- 5 x - 2 = - 12$
$\textcolor{w h i t e}{\ldots . .} + 2 \textcolor{w h i t e}{} + 2$ $\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .}$ $\textcolor{w h i t e}{\ldots \ldots \ldots} + 2 \textcolor{w h i t e}{\ldots \ldots .} + 2$

$- 5 x = 14$ $\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .}$ $- 5 x = - 10$
$\frac{\textcolor{w h i t e}{1}}{-} 5 \textcolor{w h i t e}{\ldots} \frac{\textcolor{w h i t e}{1}}{-} 5$ $\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .}$ $\frac{\textcolor{w h i t e}{1}}{-} 5 \textcolor{w h i t e}{\ldots \ldots .} \frac{\textcolor{w h i t e}{1}}{-} 5$

$x = - \frac{14}{5}$ $\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .}$ $x = 2$

So, $x$ is $- \frac{14}{5}$ or $2$ . If we want to, we can double check our answers by graphing the equation and see the $x$-intercepts.

graph{abs(-5x-2)-12=y}

We got it right!! Great job.