# How do you solve -2|-5x + 2| + 2 = -74?

Feb 27, 2017

$x = - 7.2 , 8$

#### Explanation:

Start rearranging the bits outside of the modulus:

$- 2 | - 5 x + 2 | + 2 = - 74$
$| - 5 x + 2 | = \frac{- 76}{- 2} = 38$

A modulus is a positive or negative become positive. There are two ways to solve it.

Firstly, you can square both sides, because either positive or negative numbers squared become positive. However, ${38}^{2}$ is a big number, so this is considerably more difficult than the second method.

Solve two equations, a positive and a negative.

1) $- 5 x + 2 = 38$
2) $- 5 x + 2 = - 38$

Now solve each:

1) $- 5 x + 2 = 38$
$- 5 x = 36$
$x = - 7.2$

2) $- 5 x + 2 = - 38$
$- 5 x = - 40$
$x = 8$

So now you have your solutions:

$x = - 7.2 , + 8$