Solving Absolute Value Inequalities

Jan 26, 2026

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This guide covers the fundamentals of solving absolute value inequalities, including critical definitions and the methods for approaching them. Learn about the principles of "less than" and "greater than" cases, making independent case analyses. Practice with specific examples such as solving |2x + 3| < 6 and |2x – 3| > 5. Discover how to express combined inequalities as absolute value statements, and get ready to tackle practice challenges. Essential resources for additional help are also included.

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Solving Absolute Value Inequalities

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Solving Absolute Value Inequalities -a 0 a -a 0 a Definition: Definition:
Less ThAND GreatOR AND OR Keys to Solving Absolute Value Inequalities
GreatOR OR OR
Less ThAND AND AND
Your Turn… Solve | 2x + 3 | < 6. Make two cases. Solve the two cases independently.
Your Turn… Solve | 2x – 3 | > 5. Make two cases. Solve the two cases independently.
Find the absolute-value inequality statement that corresponds to the inequality –2 < x < 4. Challenges… HINT: Think midpointand distance. Find the absolute-value inequality statement that corresponds to the inequalities x < 19 or x > 24.
www.my.hrw.com/ More Help??? http://www.purplemath.com/modules/absineq.htm Your user name and password. http://regentsprep.org/Regents/mathb/7D8/absinequal.htm