# How do you solve abs(2x - 3) = 6?

Mar 22, 2018

$x = 4.5$ and $x = - 1.5$

#### Explanation:

By definition of absolute value, whatever is inside can be $6$ or $- 6$.

This gives us two equations:
$2 x - 3 = 6$
$2 x - 3 = - 6$

Solving the first equation,
$2 x - 3 = 6$
$2 x = 9$
$x = 4.5$

Solving the second equation,
$2 x - 3 = - 6$
$2 x = - 3$
$x = - 1.5$

So the two values of x are 4.5 and -1.5