Absolute Value Inequalities Practice Test

About This Absolute Value Inequalities Practice Test

This 20-question test treats absolute value as distance. Questions ask you to solve inequalities, recognize inside and outside solution sets, convert answers to interval notation, handle impossible or universal cases, and reconstruct an inequality from its endpoints.

The set includes direct forms such as $|x-h|<r$, expressions that must first be isolated or factored, and verbal distance descriptions. Worked explanations emphasize the center, radius, endpoint type, and correct use of “and” or “or.”

Inside and Outside Patterns

• Less than or less than or equal to produces one inside interval.
• Greater than or greater than or equal to produces two outside intervals.
• Strict symbols use open endpoints; inclusive symbols use closed endpoints.
• An absolute value cannot be negative, which creates useful special cases.

Suggested Method

1. Isolate the absolute-value expression.
2. Check whether the right side is positive, zero, or negative.
3. Choose an inside compound inequality or two outside inequalities.
4. Solve every part and preserve strict or inclusive endpoints.
5. Test the midpoint and an outside point when the direction is uncertain.

Common Errors

Students often reverse “and” and “or,” forget to reverse an inequality after multiplying by a negative number, use the wrong center for an expression such as $|x+3|$, or use brackets for a strict inequality.

Practice Format

The questions move from direct solution sets to interpretation and reverse construction. Instant explanations are available after every answer, and the final score is calculated from all 20 items.