# How do you solve abs(2x-3)=5?

Jun 19, 2018

$x = - 1$

$x = 4$

#### Explanation:

As explained below:

Step 1: Clear the absolute value bars

$| 2 x - 3 | = 5$

For negative part, lets use $- \left(2 x - 3\right)$

For positive part, lets use $\left(2 x - 3\right)$

Step 2: Solve the negative part

$- \left(2 x - 3\right) = 5$

$- 2 x + 3 = 5$

$- 2 x = 5 - 3$

$- 2 x = 2$

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

$x = - 1$ ----> solution for the negative part

Step 3: Solve the positive part

$\left(2 x - 3\right) = 5$

$2 x = 5 + 3$

$2 x = 8$

$x = \frac{8}{2}$

$x = 4$ ------> solution for the positive part

So values of x are $x = - 1$ and $x = 4$

Jun 19, 2018

$x = - 1 \text{ or } x = 4$

#### Explanation:

$\text{the expression inside the absolute value can be positive}$
$\text{or negative}$

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

$2 x - 3 = 5 \Rightarrow 2 x = 5 + 3 = 8 \Rightarrow x = 4$

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

$- \left(2 x - 3\right) = 5$

$- 2 x + 3 = 5$

$- 2 x = 5 - 3 = 2$

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

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

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

$x = - 1$

$| - 2 - 3 | = | - 5 | = 5$

$x = 4$

$| 8 - 3 | = | 5 | = 5$

$x = - 1 \text{ or "x=4" are the solutions}$