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Chapter 1: Problem 55

Solve each compound inequality. $$-11<2 x-1 \leq-5$$

Short Answer

Expert verified
The solution to the compound inequality is \(-5 < x \leq -2\).

Step by step solution

01

Split the Compound Inequality

Divide the compound inequality into two separate ones: i. \(-11 < 2x - 1\) and ii. \(2x - 1 \leq -5\)
02

Solve the first inequality

For the first inequality \(-11 < 2x - 1\), add 1 to both sides to isolate \(2x\), leading to \(-10 < 2x\). Then, divide both sides by 2 to solve for \(x\), so \(x > -5\).
03

Solve the second inequality

For the second inequality \(2x - 1 \leq -5\), add 1 to both sides to isolate \(2x\), leading to \(2x \leq -4\). Then, divide both sides by 2 to solve for \(x\), so \(x \leq -2\).
04

Combine Solutions

Now, combine the solutions of the two inequalities to find the intersection. The previous two steps gave us \(x > -5\) and \(x \leq -2\), both hold true for the solution which is \(-5 < x \leq -2\)

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