# How do you solve the inequality abs(3x+5)+2<1 and write your answer in interval notation?

Aug 20, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{2}$ from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

$\left\mid 3 x + 5 \right\mid + 2 - \textcolor{red}{2} < 1 - \textcolor{red}{2}$

$\left\mid 3 x + 5 \right\mid + 0 < - 1$

$\left\mid 3 x + 5 \right\mid < - 1$

The absolute value function takes any number and transforms it into its non-negative form. Therefore, the result of an absolute value function cannot be negative and therefore cannot be $\textcolor{red}{< - 1}$.

So, there is no answer to this question. Or, the answer is the empty or null set: $\left\{\emptyset\right\}$