# How do you solve  |4x-2|=6?

Apr 9, 2016

$x = - 1 , 2$

#### Explanation:

The procedure is to separate the equation in two branches:

1) if 4x-2>0:

$| 4 x - 2 | = 6 \mathmr{and} 4 x - 2 > 0$

$4 x - 2 = 6 \mathmr{and} 4 x > 2$

$4 x = 6 + 2 \mathmr{and} x > \frac{2}{4}$

$x = \frac{8}{4} \mathmr{and} x > \frac{2}{4}$

$x = 2 \mathmr{and} x > \frac{1}{2}$

$x = 2$

2) if 4x-2<0:

$| 4 x - 2 | = 6 \mathmr{and} 4 x - 2 < 0$

$- 4 x + 2 = 6 \mathmr{and} 4 x < 2$

$- 4 x = 6 - 2 \mathmr{and} x < \frac{2}{4}$

$x = - \frac{4}{4} \mathmr{and} x < \frac{2}{4}$

$x = - 1 \mathmr{and} x < \frac{1}{2}$

$x = - 1$