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Chapter 1: Problem 57

Solve each compound inequality. $$-3 \leq \frac{2}{3} x-5<-1$$

Short Answer

Expert verified
The solution to the compound inequality \( -3 \leq \frac{2}{3} x-5<-1 \) is \( 3 \leq x < 6 \).

Step by step solution

01

Split the Compound Inequality

The compound inequality -3 鈮� (2/3)x - 5 < -1 can be divided into the two inequalities:\n-3 鈮� (2/3)x - 5 and (2/3)x - 5 < -1
02

Solve the First Inequality

To solve -3 鈮� (2/3)x - 5, first add 5 to both sides of the inequality to get 2 鈮� (2/3)x. Then, multiply both sides of the inequality by 3/2 to get: \(x \geq 3\)
03

Solve the Second Inequality

To solve (2/3)x - 5 < -1, add 5 to both sides of the inequality: (2/3)x < 4. Then, multiply both sides of the inequality by 3/2. This gives: \(x < 6\)
04

Combine the Solutions

Now, combine the solutions from steps 2 and 3 to find the solution set for the original compound inequality. So, the solution is \(3 \leq x < 6\).

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