# How do you solve 4|x + 5| + -6 = 34?

Apr 19, 2017

$x = 5 , x = - 15$

#### Explanation:

Given: $4 | x + 5 | + - 6 = 34$

Start by adding $6$ to both sides of the equation:

$4 | x + 5 | + - 6 + 6 = 34 + 6$

Simplify: $4 | x + 5 | = 40$

Divide both sides by $4$: $\frac{4 | x + 5 |}{4} = \frac{40}{4}$

Simplify: $| x + 5 | = 10$

Break the function into two equations:
$y = | x + a | \text{ is " y = x +a" and } y = - \left(x + a\right)$

$| x + 5 | = 10 \text{ is " x+5 = 10 " and } - \left(x + 5\right) = 10$

Solve each equation:

$x + 5 = 10$
$x + 5 - 5 = 10 - 5$
$x = 5$

$- \left(x + 5\right) = 10$
$- x - 5 = 10$
$- x - 5 + 5 = 10 + 5$
$- x = 15$
$x = - 15$

$4 | 5 + 5 | + - 6 = 4 \cdot 10 - 6 = 40 - 6 = 34$
$4 | 5 + - 15 | + - 6 = 4 | - 10 | - 6 = 4 \left(10\right) - 6 = 34$