Question

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Question: Solve$\mathbf{-}\mathbf{4}\mathbf{<}\mathbf{3}\mathit{x}\mathbf{+}\mathbf{8}\mathbf{\le }\mathbf{23}$

Short answer

The solution of the given compound inequality$-4<3x+8\le 23$is$x\in \left(-4,5\right]$

Step-by-step solution

Step 1. Solve the given compound inequality −4<3x+8≤23

The solution of the given compound inequality $-4<3x+8\le 23$is:

$\begin{array}{c}-4<3x+8\le 23\\ -4-8<3x+8-8\le 23-8\\ -12<3x\le 15\\ \frac{-12}{3}<\frac{3x}{3}\le \frac{15}{3}\\ -4<x\le 5\end{array}$

Step 2. Write the solution of the given compound inequality −4<3x+8≤23.

The solution in interval notation is $x\in \left(-4,5\right]$

Therefore, the solution of the compound inequality$-4<3x+8\le 23$is$x\in \left(-4,5\right]$