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

Apr 8, 2017

$x = \frac{1}{3} \text{ or } x = 5$

#### Explanation:

There are 2 possible solutions to the equation.

$2 x - 3 = \textcolor{red}{\pm} \left(x + 2\right)$

$\textcolor{b l u e}{\text{first solution}}$

$2 x - 3 = x + 2$

$\text{subtract x from both sides.}$

$2 x - x - 3 = \cancel{x} \cancel{- x} + 2$

$\Rightarrow x - 3 = 2$

$\text{add 3 to both sides.}$

$x \cancel{- 3} \cancel{+ 3} = 2 + 3$

$\Rightarrow x = 5$

$\textcolor{b l u e}{\text{second solution}}$

$2 x - 3 = - x - 2$

$\Rightarrow 3 x = 1$

$\Rightarrow x = \frac{1}{3}$

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

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

$\text{left side } = | \left(2 \times 5\right) - 3 | = | 7 | = 7$

$\text{right side } = | 5 + 2 | = | 7 | = 7$

$\text{left side } = | \frac{2}{3} - 3 | = | - 2 \frac{1}{3} | = 2 \frac{1}{3}$

$\text{right side } = | \frac{1}{3} + 2 | = | 2 \frac{1}{3} | = 2 \frac{1}{3}$

$\Rightarrow x = \frac{1}{3} \text{ or " x=5" are the solutions}$