# Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 53

$(-5, -2]$

#### Work Step by Step

The idea is to isolate x on one side. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $-11 \lt 2x-1\leq-5 \qquad$ ... add 1 to all $-10 \lt 2x\leq-4 \qquad$ ... divide with 2 $-5 \lt x\leq-2$ ... left border excluded, right border included. The solution set is $(-5, -2]$.

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