# How do you solve  abs(4x - 2) = 10 ?

Aug 8, 2015

$x = 3$ or $x = - 2$.

#### Explanation:

You're dealing with an absolute value equation, which means that you need to take into account two possibilities for the modulus

• if $4 x - 2 \ge 0$, you have

$| 4 x - 2 | = 4 x - 2$

and the equation becomes

$4 x - 2 = 10$

$4 x = 12 \implies x = \frac{12}{4} = \textcolor{g r e e n}{3}$

• If $4 x - 2 < 0$, then you have

$| 4 x - 2 | = - \left(4 x - 2\right) = - 4 x + 2$

and the equation becomes

$- 4 x + 2 = 10$

$- 4 x = 8 \implies x = \frac{8}{- 4} = \textcolor{g r e e n}{- 2}$

So, your equation has two possible solutions: $x = 3$ or $x = - 2$.