# How do you solve 4|-6x + 6| + -3 = 93?

Dec 5, 2016

$x = - 3$ and $x = 5$

#### Explanation:

When solving an absolute value problem the first step is to isolate the absolute value on one side of the equation:

$4 \left\mid - 6 x + 6 \right\mid + - 3 + 3 = 93 + 3$

$4 \left\mid - 6 x + 6 \right\mid + 0 = 96$

$4 \left\mid - 6 x + 6 \right\mid = 96$

$\frac{4 \left\mid - 6 x + 6 \right\mid}{4} = \frac{96}{4}$

$\frac{\cancel{4} \left\mid - 6 x + 6 \right\mid}{\cancel{4}} = 24$

$\left\mid - 6 x + 6 \right\mid = 24$

Now because the absolute value function converts both negative and positive numbers to a negative number we must solve the term within the absolute value for both $24$ and $- 24$:

$- 6 x + 6 = 24$

$- 6 x + 6 - 6 = 24 - 6$

$- 6 x + 0 = 18$

$- 6 x = 18$

$\frac{- 6 x}{-} 6 = \frac{18}{- 6}$

$\frac{\cancel{- 6} x}{\cancel{- 6}} = - 3$

$x = - 3$

and

$- 6 x + 6 = - 24$

$- 6 x + 6 - 6 = - 24 - 6$

$- 6 x + 0 = - 30$

$- 6 x = - 30$

$\frac{- 6 x}{-} 6 = \frac{- 30}{- 6}$

$\frac{\cancel{- 6} x}{\cancel{- 6}} = 5$

$x = 5$