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MathAlgebra

Absolute Value Inequalities: Solve |−2x + 7| ≤ 13

Solve the absolute value inequality |−2x + 7| ≤ 13. Reverse the inequality signs when dividing by −2 and confirm the closed interval [−3, 10].

Question

Find the solution set of the absolute value inequality and express it in interval notation:

∣−2x+7∣≤13.|-2x+7|\le 13.

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Evidence boundary

This page solves OpenStax Algebra and Trigonometry 2e, Section 2.7, Exercise 20, over the real numbers. It preserves the negative coefficient, constants and non-strict inequality. The interval and endpoint checks are derived here; the exercise does not require a graph.