# How do you graph and solve |2x – 3| – 6 = –1?

Dec 2, 2017

$- 1 = x = 4$

#### Explanation:

When you have an absolute value equation, you isolate the absolute value before trying anything else.
$| 2 x - 3 | - 6 = - 1$ becomes
$| 2 x - 3 | = 5$
We have to note that there are two solutions to absolute value equations, since $| - a | = a$ and $| a | = a$
In other words, $2 x - 3 = 5$ and $2 x - 3 = - 5$ both give you the final answer of $| 2 x - 3 | = 5$.
$2 x - 3 = 5$
$2 x = 8$
$x = 4$

$2 x - 3 = - 5$
$2 x = - 2$
$x = - 1$
When we plug in these values, we find out that they both work. Therefore, $- 1 = x = 4$