Question

Solve each inequality, graph the solution, and write the solution in interval notation.

$-8<5x+2\le -3$

Short answer

Solution of inequality:

$-2<x\le -1$

Graph the numbers that make both inequalities true:

The solution in interval notation:

$(-2,-1]$

Step-by-step solution

Step 1. Given information  

Consider the inequality

$-8<5x+2\le -3$

Step 2. Solve the inequality  −8 < 5x + 2 ≤ −3

Subtract 2 to all three parts:

$-8-2<5x+2-2\le -3-2$

Simplify:

$-10<5x\le -5$

Divide each part by 5:

$\frac{-10}{5}<\frac{5x}{5}\le \frac{-5}{5}$

Simplify:

$-2<x\le -1$

Step 3. Graph the solution of inequality  −2 < x ≤ −1

The solution in interval notation:

$(-2,-1]$