# How do you solve |-4x + -1| = 33?

Jun 27, 2016

$x = - \frac{17}{2}$ and $x = 8$

#### Explanation:

$| - 4 x - 1 | = 33$

let's assume that $- 4 x - 1 > 0$ so #|-4x - 1| = -4x -1

so we look at
$- 4 x - 1 = 33 \setminus \implies 4 x = - 34 \setminus \implies x = - \frac{17}{2}$

then let's assume that in fact $- 4 x - 1 < 0$ so $| - 4 x - 1 | = 4 x + 1$

so here instead we look at
$4 x + 1 = 33 \setminus \implies 4 x = 32 \setminus \implies x = 8$