7th Grade Two-Step Inequalities Test Solutions and Scoring (PDF)
This grade 7 inequalities test answers for 7th Grade covers two-step inequalities (Common Core 7.EE.B.4b), with a free PDF to print.
Use this answer key and scoring guide to grade the inequalities test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.
Grade 7 · Common Core State Standards: 7.EE.B.4b
Grade 7 inequalities test answers: worked solutions
Question 1 – Two-step inequality [2 pts]
Subtract \(5\) from both sides: \(3x< 15\)
Divide both sides by \(3\): \(x< 5\)
Check a value in the solution set: \(x=4\) gives \(17< 20\), which is true.
\(x< 5\)
Scoring: 1 point for the solution (including the correct symbol); 1 point for the graph with the correct circle and shading.
Question 2 – Reverse the symbol [2 pts]
Subtract \(3\) from both sides: \(-4x\ge-16\)
Divide both sides by \(-4\) and reverse the inequality symbol: \(x\le4\)
Check a value in the solution set: \(x=3\) gives \(-9\ge-13\), which is true.
\(x\le4\)
Scoring: 1 point for the solution (including the correct symbol); 1 point for the graph with the correct circle and shading.
Question 3 – Write from a graph [2 pts]
The graph shows \(x>3\) (open circle, shading right).
3 is not a solution; 3.5 is a solution.
\(x>3\)
Scoring: 1 point for the inequality; 1 point for the correct decisions.
Question 4 – Word problem [2 pts]
\(3-0.25p\ge 1\), \(-0.25p\ge -2\), \(p\le 8\).
at most 8 pencils
Scoring: 1 point for the inequality; 1 point for the solution with meaning.
Question 5 – Check solutions [2 pts]
\(5(3)-8=7\le 12\) true.
\(5(4)-8=12\le 12\) true.
\(5(5)-8=17\le 12\) false.
3 and 4 are solutions; 5 is not
Scoring: 1 point for the tests; 1 point for the conclusions.
Question 6 – Find the error [2 pts]
Noah divided by a negative number but did not reverse the symbol.
\(x<-4\)
\(x<-4\)
Scoring: 1 point for the explanation; 1 point for the correct solution.
Question 7 – Phone plan [2 pts]
\(0.06m+20\le 27.5\), \(0.06m\le 7.5\), \(m\le 125\).
at most 125 minutes
Scoring: 1 point for the inequality; 1 point for the solution.
Question 8 – Weight limit [3 pts]
- \(6.5b+10\le 50\)
- \(6.5b\le 40\), so \(b\le 6.15\) (about).
- 6 boxes.
Scoring: 1 point for each part.
Question 9 – Compare plans [3 pts]
- \(5+0.5s< 1.25s\)
- \(5< 0.75s\), so \(s>6.67\) (about).
- Plan A is cheaper when the customer buys 7 or more songs a month.
Scoring: 1 point for each part.
Total score
20 points
Key facts behind this grade 7 inequalities test answers
- 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 answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
All Grade 7 chapters: Grade 7 math.
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