Question

as you solve the problems below, consider what would result in a compound inequality with only one bound. solve the following inequalities, and graph each solution on a number line. 1. 3x - 3 < x + 5 < 2 - 2x a 3x - 3 < x + 5 subtract x on both b x + 5 < 2 - 2x

Explanation:

Step1: Solve left - hand inequality

Subtract \(x\) from both sides of \(3x - 3

Step2: Solve right - hand inequality

Add \(2x\) to both sides of \(x + 5<2-2x\), we have \(x+2x + 5<2-2x+2x\), which simplifies to \(3x+5<2\). Subtract 5 from both sides: \(3x+5 - 5<2 - 5\), so \(3x<-3\). Divide both sides by 3: \(x<-1\).

Step3: Combine the solutions

The compound inequality \(3x - 3

Answer:

The solution of the inequality \(3x - 3