# How do you solve |3x+8|+2=7?

Jul 7, 2016

$x = - 1 , x = - \frac{13}{3}$

#### Explanation:

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

|5| = 5 and |- 5| = 5

The$\textcolor{m a \ge n t a}{\text{ absolute value of both 5 and -5 is 5}}$

This is because the absolute value is a measure of how far a value is from the origin , but doesn't consider direction. -5 and 5 are both 5 units from the origin.

However, when there are variables inside the 'bars' we don't know if the value is positive or negative and so must consider both options.

Thus for |3x + 8 | + 2 = 7

We must consider $\textcolor{red}{\text{3x+8+2=7}}$

and $\textcolor{b l u e}{\text{-(3x+8)+2=7}}$

$\Rightarrow \textcolor{red}{\text{3x=7-2-8"tocolor(red)"3x=-3" tocolor(red)"x=-1}}$

$\Rightarrow \textcolor{b l u e}{\text{-3x-8+2=7"tocolor(blue)"-3x=7-2+8"tocolor(blue)"x=-13/3}}$