Multi-Step Inequalities Practice Test

About This Multi-Step Inequalities Practice Test

This test moves beyond one-step inequalities and requires students to simplify expressions before isolating the variable. Problems include parentheses, fractional coefficients, decimal coefficients, variables on both sides, and nested grouping symbols.

The final questions add compound inequalities, absolute values, identities, contradictions, and interval interpretation. The set is suitable for Algebra 1 review, high school placement practice, and ACT-style algebra preparation.

Skills Covered

Distributing correctly, combining like terms, clearing denominators, reversing an inequality after division by a negative number, solving AND and OR statements, and recognizing no-solution or all-real-number outcomes.

Key Rules

1. Perform the same operation on both sides.
2. Reverse the inequality only when multiplying or dividing by a negative number.
3. For |A| ≤ c, solve −c ≤ A ≤ c; for |A| > c, solve A < −c or A > c.
4. When the variable cancels, inspect whether the remaining statement is always true or always false.

Common Mistakes to Avoid

Do not reverse the sign after adding a negative number, cancel terms across addition, forget to distribute a minus sign, or change a strict inequality into a non-strict inequality.

Practice Format

Immediate feedback shows the correct interval and explains why each distractor reflects a common algebra error.