Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a two-step inequalities test? Then this Grade 7 test on Solving and Graphing Two-Step Inequalities checks the whole chapter, with points for each question. This test covers solving and graphing two-step inequalities, including negative coefficients, decimals and fractions, and interpreting solutions in real situations. Show every step and mark any sign reversal. Calculators are not allowed. Plan on 45 minutes for the 8 questions.
Standards: 7.EE.B.4b · Level: Grade 7
Question 1 Solve and Graph (2 points)
Solve 5x − 8 > 22 and graph the solution on the number line.
Question 2 Negative Coefficient (2 points)
Solve −3x + 7 < −8.
Question 3 Decimal Inequality (2 points)
Solve 0.4x − 1.6 < 2.4.
Question 4 Negative Factor Outside (3 points)
Consider −4(x + 2) < 20.
- Solve the inequality. (2 points)
- Explain why the direction of the inequality sign changed. (1 point)
Question 5 Fraction and Negative (3 points)
Solve −34x − 2 > 4. Show every step.
Question 6 Transit Card (3 points)
Teresa has $85 on a transit card. Each ride costs $2.75. She wants more than $30 left on the card after r rides.
- Write an inequality for r. (1 point)
- Solve the inequality. (1 point)
- State the greatest whole number of rides she can take. (1 point)
Question 7 Reading a Graph (3 points)
The graph shows the solution set of a two-step inequality.
- Write the solution as an inequality. (1 point)
- Is −2 a solution? Explain. (1 point)
- Show that 3x + 4 > −2 has this solution set. (1 point)
Question 8 Find the Mistake (2 points)
Kai solved −6x + 5 > 29 and wrote: −6x > 24, so x > −4.
- Identify his error. (1 point)
- Write the correct solution. (1 point)
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