# How do you solve 5=|2x— 4|?

Feb 19, 2016

$\left\{- \frac{1}{2} , \frac{9}{2}\right\}$

#### Explanation:

Note: Whenever you have an absolute value equation, there is a possibility of 2 solutions.

Because, $| x | = - x \text{ " "or" " } x$

Given : $5 = | 2 x - 4 |$

Step 1: Remove the absolute value sign, we will have TWO equation like this

a) $5 = 2 x - 4 \text{ " " " "or" " " }$b) $- 5 = 2 x - 4$

Step 2: Solve each equation like this

a) $\text{ " 5 } = 2 x - 4$

$+ 4 \text{ } + 4$
$- - - - - -$

$9 \text{ } = 2 x$

$\frac{9}{2} = \frac{2 x}{2}$
$x = \frac{9}{2}$

Try to solve for (b), and you should get $x = - \frac{1}{2}$

Answer: $x = - \frac{1}{2} , \frac{9}{2}$