How do you solve |8x + 4| = 52?

Oct 30, 2017

$x = 6 \mathmr{and} x = - 7$

Explanation:

$| 8 x + 4 | = 52$
Solve for the absolute value
We know either $8 x + 4 = 52 \mathmr{and} 8 x + 4 = - 52$
We gonna call the first one possibility ONE and the second one possibility TWO.

Let's start by solving the first possibility
$8 x + 4 = 52$
Subtract $\textcolor{red}{4}$ from both sides
$8 x \cancel{+ 4} \cancel{\textcolor{red}{- 4}} = 52 - \textcolor{red}{4}$
$8 x = 48$
Divide both sides $8$
$\frac{\cancel{8} x}{\cancel{8}} = \frac{48}{8}$
$x = 6$

Then, solve the second possibility
$8 x + 4 = - 52$
Let's start by subtracting $\textcolor{red}{4}$ from both sides
$8 x \cancel{+ 4} \cancel{\textcolor{red}{- 4}} = - 52 - \textcolor{red}{4}$
$8 x = - 56$
Divide both sides by $8$
$\frac{\cancel{8} x}{\cancel{8}} = \frac{- 56}{8}$
$x = - 7$

Thus,

The answer is $x = 6 \mathmr{and} x = - 7$