# How do you solve |(3x + 4 )/ 6| = |-4|?

Apr 24, 2017

$\text{For}$ $| \frac{3 x + 4}{6} | = | - 4 |$

$x = \frac{20}{3} , - \frac{28}{3}$

#### Explanation:

For absolute value you are going to solve for positive and negative.
Like this.

$| \frac{3 x + 4}{6} | = | - 4 |$

So we are solving

$| \frac{3 x + 4}{6} | = 4$ $\textcolor{red}{\text{AND}}$ $| \frac{3 x + 4}{6} | = - 4$

$\textcolor{red}{| \frac{3 x + 4}{6} | = 4}$

Multiply both sides by six to remove denominator
$\frac{3 x + 4}{\cancel{6}} = 4 \cdot 6$

$3 x + 4 = 24$

Subtract 4 from both sides
$3 x \cancel{+ 4} = 24 - 4$
$3 x = 20$

Divide by 3 so that we have "x" alone
$\frac{\cancel{3} x}{\cancel{3}} = \frac{20}{3}$

$x = \frac{20}{3}$

Now, $\textcolor{red}{| \frac{3 x + 4}{6} | = - 4}$

This is the same process so I'll go through it a little quicker.

$| \frac{3 x + 4}{\cancel{6}} | = - 4 \cdot 6$

$3 x + 4 = - 24$

$3 x \cancel{+ 4} = - 24 - 4$

$3 x = - 28$

$x = - \frac{28}{3}$