# How do you solve the inequality abs(2x+1)-5<0 and write your answer in interval notation?

Aug 25, 2017

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{5}$ to each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

$\left\mid 2 x + 1 \right\mid - 5 + \textcolor{red}{5} < 0 + \textcolor{red}{5}$

$\left\mid 2 x + 1 \right\mid - 0 < 5$

$\left\mid 2 x + 1 \right\mid < 5$

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

$- 5 < 2 x + 1 < 5$

Next, subtract $\textcolor{red}{1}$ from each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$- 5 - \textcolor{red}{1} < 2 x + 1 - \textcolor{red}{1} < 5 - \textcolor{red}{1}$

$- 6 < 2 x + 0 < 4$

$- 6 < 2 x < 4$

Now, divide each segment of the system by $\textcolor{red}{2}$ to solve for $x$ while keeping the system balanced:

$- \frac{6}{\textcolor{red}{2}} < \frac{2 x}{\textcolor{red}{2}} < \frac{4}{\textcolor{red}{2}}$

$- 3 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} < 2$

$- 3 < x < 2$

Or

$x > - 3$ and $x < 2$

Or, in interval notation:

$\left(- 3 , 2\right)$