# What is the solution set for abs(2x – 3) – 10 = –1?

Aug 5, 2015

$x = \left\{- 3 , 6\right\}$

#### Explanation:

Start by isolating the modulus on one side of the equation

$| 2 x - 3 | - \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} = - 1 + 10$

$| 2 x - 3 | = 9$

You are going to look at two cases for this equation

• $\left(2 x - 3\right) > 0$, which means that you have

$| 2 x - 3 | = 2 x - 3$

and the equation is

$2 x - 3 = 9$

$2 x = 12 \implies x = \frac{12}{2} = \textcolor{g r e e n}{6}$

• $\left(2 x - 3\right) < 0$, which will get you

$| 2 x - 3 | = - \left(2 x - 3\right) = - 2 x + 3$

and the equation is

$- 2 x + 3 = 9$

$- 2 x = 6 \implies x = \frac{6}{- 2} = \textcolor{g r e e n}{- 3}$

Because you have no restriction for the values of $x$ that you make for extraneous solutions, both values are valid solutions.