Two-Step Inequalities: Grade 7 Math Test – PDF Download

Question 1: Solve and graph (2 points)

Solve \(3x+4>19\). Graph the solution on the number line.

Question 2: Negative coefficient (2 points)

Solve \(-5x-3\le 12\). Graph the solution on the number line.

Question 3: Testing values (2 points)

Consider the inequality \(4x-7< 5\). Tell whether each value is a solution.

1. \(x=2\) (1 point)
2. \(x=3\) (1 point)

Question 4: Find the error (2 points)

Ethan solved \(-4x+6>22\) like this: \(-4x>16\), so \(x>-4\). Explain his mistake and give the correct solution.

Question 5: Fraction coefficient (2 points)

Solve \(\frac{x}{4}-3\ge 2\).

Question 6: Reading a graph (2 points)

The graph shows the solution set of an inequality.

1. Write the inequality that the graph shows. (1 point)
2. Complete a two-step inequality with this solution set: \(2x+1\ge\) ___ . (1 point)

Question 7: Saving for a skateboard (3 points)

Liam has \(\$40\) and saves \(\$6\) each week. He needs more than \(\$100\) for a skateboard.

1. Write an inequality for the number of weeks \(w\). (1 point)
2. Solve the inequality. (1 point)
3. What is the fewest whole number of weeks Liam must save? (1 point)

Question 8: Freezer cooling (3 points)

A freezer starts at \(8^{\circ}\text{F}\) and cools by \(4^{\circ}\text{F}\) every hour.

1. Write an inequality for the number of hours \(h\) until the temperature is below \(-12^{\circ}\text{F}\). (1 point)
2. Solve it. (1 point)
3. Interpret the solution in a sentence. (1 point)

Question 9: Solve with a leading constant (2 points)

Solve \(7-2x\ge 15\).

⬇ Download the Grade 7 Two-Step Inequalities test (PDF, 87 KB)

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