Compound Inequalities Practice Test

Solve intersections and unions, reverse signs correctly, use interval notation, and recognize empty or universal solution sets.

Compound Inequalities Practice Test

20 varied compound-inequality questions with instant explanations.

About This Compound Inequalities Practice Test

Compound inequalities combine two conditions. An AND statement requires overlap between solution sets, while an OR statement accepts values from either set. This test includes chained inequalities, separately written conditions, interval notation, number-line descriptions, and contextual restrictions.

Several questions require dividing by a negative number, which reverses every affected inequality sign. Other questions highlight no-solution, all-real, and single-point cases so students learn to analyze the relationship between the two component sets rather than applying a single mechanical rule.

Compound-Inequality Skills Covered

The test covers three-part inequalities, intersections, unions, sign reversal, endpoint notation, interval conversion, graph interpretation, contradictory conditions, universal unions, equal outer bounds, and real-world ranges.

How to Approach the Questions

  1. Preserve the original connector: AND means intersection, OR means union.
  2. In a chained inequality, apply each algebraic operation to all three parts.
  3. Reverse inequality signs whenever multiplying or dividing by a negative number.
  4. Check endpoints separately and translate strict versus inclusive symbols accurately.

Common Mistakes to Avoid

Common errors include changing AND to OR, failing to reverse signs after division by a negative, swapping open and closed endpoints, shading the complement, ignoring one branch, and assuming every compound inequality produces a nonempty interval.

Practice Format

Use this free 20-question test for Algebra 1, ACT-style review, classroom assignments, intervention practice, or independent study.