7th Grade Two-Step Inequalities Test with Point Values (PDF)

7th Grade math test: Two-Step Inequalities – Maths PDF

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This grade 7 inequalities test for 7th Grade covers two-step inequalities (Common Core 7.EE.B.4b), with a free PDF to print.

This 45-minute test checks solving two-step inequalities, graphing solution sets on a number line, and interpreting solutions in context (Common Core 7.EE.B.4b). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Two-Step Inequalities
Standards: 7.EE.B.4b
Time: 45 minutes
Total: 20 points

Grade 7 inequalities test: questions

Question 1 – Two-step inequality [2 pts]

Solve $3x+5< 20$ and graph the solution.

Question 2 – Reverse the symbol [2 pts]

Solve $-4x+3\ge-13$ and graph the solution.

Question 3 – Write from a graph [2 pts]

A graph.

Write the inequality shown by the graph. Then decide whether $3$ and $3.5$ are solutions.

Question 4 – Word problem [2 pts]

A school store sells pencils for $0.25 each. Ethan has $3 and wants to keep at least $1. Write and solve an inequality for the number of pencils p.

Question 5 – Check solutions [2 pts]

Which of these values are solutions of $5x-8\le 12$? Show the test for each: $x=3$, $x=4$, $x=5$.

Question 6 – Find the error [2 pts]

Noah solved $-2x>8$ and wrote $x>-4$. Explain his mistake and give the correct solution.

Question 7 – Phone plan [2 pts]

A plan costs $20 plus $0.06 per minute. Priya can spend at most $27.50. Write and solve an inequality for the minutes m.

Question 8 – Weight limit [3 pts]

A shipping limit.

A delivery bike can carry at most 50 pounds. A bag weighs 10 pounds and each box weighs 6.5 pounds. (a) Write an inequality for the number of boxes b. (1 point) (b) Solve it. (1 point) (c) State the greatest number of boxes the bike can carry. (1 point)

Question 9 – Compare plans [3 pts]

Two music plans.

(a) Write an inequality that says Plan A is cheaper than Plan B for s songs. (1 point) (b) Solve it. (1 point) (c) Explain what the solution means for a customer. (1 point)

Key facts behind this grade 7 inequalities test

Key facts

Solve $px + q > r$ with the same steps as an equation.
Reverse the symbol when you multiply or divide both sides by a negative number.
Use an open circle for $<$ and $>$, and a closed circle for $\le$ and $\ge$.
Shade the side of the number line that contains the solutions.
Interpret the solution set in the context of the problem.

How to use this grade 7 inequalities test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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