# How do you solve abs(2x-9)=11?

Jan 25, 2017

See the entire solution process below:

#### Explanation:

Equations with an absolute value function are a special case giving two solutions. The absolute value function takes any negative or positive term and transforms it into its positive form. Therefore, you must solve the term inside the absolute value function for both the negative and positive value it is equated to.

Solution 1)

$2 x - 9 = - 11$

$2 x - 9 + \textcolor{red}{9} = - 11 + \textcolor{red}{9}$

$2 x - 0 = - 2$

$2 x = - 2$

$\frac{2 x}{\textcolor{red}{2}} = \frac{- 2}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = - 1$

$x = - 1$

Solution 2)

$2 x - 9 = 11$

$2 x - 9 + \textcolor{red}{9} = 11 + \textcolor{red}{9}$

$2 x - 0 = 20$

$2 x = 20$

$\frac{2 x}{\textcolor{red}{2}} = \frac{20}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = 10$

$x = 10$

The solution is $x = - 1$ and $x = 10$