# How do you graph and solve | 3x + 8 | +4 <=0?

##### 1 Answer
Jul 17, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{4}$ from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

$\left\mid 3 x + 8 \right\mid + 4 - \textcolor{red}{4} \le 0 - \textcolor{red}{4}$

$\left\mid 3 x + 8 \right\mid + 0 \le - 4$

$\left\mid 3 x + 8 \right\mid \le - 4$

However, the absolute value function takes any number and converts it to $0$ or it's positive form. Therefore, the output of the absolute value function will always be $\ge 0$.

So, the absolute value of $\left(3 x + 8\right)$ cannot be less than a negative number.

So, there is no answer to this problem.

Or, the answer is the null or empty set: $\left\{\emptyset\right\}$