# What is the solution set of the equation |3-2x| = 5?

$x \setminus \in \left\{- 1 , 4\right\}$

#### Explanation:

Given equation:

$| 3 - 2 x | = 5$

$3 - 2 x = \setminus \pm 5$

$2 x = 3 \setminus \pm 5$

$x = \setminus \frac{3 \setminus \pm 5}{2}$

$x = 4 , - 1$

$x \setminus \in \left\{- 1 , 4\right\}$

Jul 27, 2018

The solutions are $S = \left\{- 1 , 4\right\}$

#### Explanation:

$3 - 2 x = 0$

$\implies$, $x = \frac{3}{2}$

There are $2$ possibilities to consider

Firstly

$- 3 + 2 x = 5$

$\implies$, $2 x = 8$

$x = 4$

And Secondly

$3 - 2 x = 5$

$\implies$, $2 x = 3 - 5$

$x = - 1$

The solutions are $S = \left\{- 1 , 4\right\}$

graph{|3-2x|-5 [-10, 10, -5, 5]}