Question

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

$-6\le 4x-2<-2$

Short answer

Solution of inequality:

$-2\le x<0$

Graph the numbers that make both inequalities true:

The solution in interval notation:

$[-2,0)$

Step-by-step solution

Step 1. Given information  

Consider the inequality

$-6\le 4x-2<-2$

Step 2. Solve the inequality   −6 ≤ 4x − 2 < −2

Add 2 to all parts:

$-6+2\le 4x-2+2<-2+2$

Simplify:

$-4\le 4x<0$

Divide each part by 4:

$\frac{-8}{4}\le \frac{4x}{4}<\frac{0}{4}$

Simplify:

$-2\le x<0$

Step 3. Graph the solution of inequality  −2 ≤ x < 0

The solution in interval notation:

$[-2,0)$