# How do you solve |2x - 5 | 6 = 12?

Feb 21, 2016

$x = \frac{7}{2} , x = \frac{3}{2}$

#### Explanation:

first write as |2x - 5 | = 2 (divide by 6 )

then 2x - 5 = 2 → 2x = 7 →$x = \frac{7}{2}$

also 2x - 5 = - 2 → 2x = 3 → $x = \frac{3}{2}$

Feb 22, 2016

$x = \frac{3}{2} , \frac{7}{2}$

#### Explanation:

First, we can divide both sides by $6$.

$\frac{\left\mid 2 x - 5 \right\mid 6}{6} = \frac{12}{6}$

$\left\mid 2 x - 5 \right\mid = 2$

This can no be split up into two separate equations because of the absolute value.

Recall that if $2 x - 5 = - 2$, then $\left\mid 2 x - 5 \right\mid = 2$ still, so we can write and solve the two following equations:

$2 x - 5 = 2$

$2 x - 5 = - 2$

Solving for each of these gives $x = \frac{7}{2}$ and $x = \frac{3}{2}$.