# How do you solve -6 + |2x – 4| = -3?

##### 1 Answer
Jan 27, 2016

$x = \left\{\frac{1}{2} , \frac{7}{2}\right\}$

#### Explanation:

Absolute value is the distance between a value and 0 on the number line

So, the distance should be always a positive integer

$- 6 + | \setminus 2 x - 4 | = - 3$

$| \setminus 2 x - 4 | = 6 - 3 = 3$

This equation is possible because the absolute value is a positive integer.

Assume 2 values:

$2 x - 4 = 3$

$2 x - 4 = - 3$

Solve for the first equation:

$2 x - 4 = 3$

$2 x = 3 + 4 = 7$

$2 x = 7$

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

So, the first value of $x$ is $\frac{7}{2}$

Now solve for second equation:

$2 x - 4 = - 3$

$2 x = 4 - 3 = 1$

$2 x = 1$

$x = \frac{1}{2}$

So, $x = \left\{\frac{1}{2} , \frac{7}{2}\right\}$