# How do you solve for x:  2|x − 3| + 4 = 6?

Apr 9, 2018

$x = 2 \text{ or } x = 4$

#### Explanation:

$\text{the expression inside the absolute value can be positive}$
$\text{or negative, hence there are 2 possible solutions}$

$\text{isolate } | x - 3 |$

$\text{subtract 4 from both sides}$

$\Rightarrow 2 | x - 3 | = 2$

$\text{divide both sides by 2}$

$\Rightarrow | x - 3 | = 1$

$\textcolor{m a \ge n t a}{\text{Positive expression}}$

$x - 3 = 1 \Rightarrow x = 1 + 3 = 4$

$\textcolor{m a \ge n t a}{\text{Negative expression}}$

$- \left(x - 3\right) = 1$

$\Rightarrow - x + 3 = 1$

$\Rightarrow - x = 1 - 3 = - 2 \Rightarrow x = 2$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the left side and if equal to the right side then they are the solutions.

$x = 2 \to 2 | - 1 | + 4 = \left(2 \times 1\right) + 4 = 6$

$x = 4 \to 2 | 1 | + 4 = \left(2 \times 1\right) + 4 = 6$

$\Rightarrow x = 2 \text{ or "x=4" are the solutions}$