Two-step Inequalities Test Answer Key with Scoring – Grade 7

Question 1 Solve and Graph (2 points)

Add 8: 5x > 30. Divide by 5: x > 6.

Scoring: 1 point for the solution, 1 point for an open circle at 6 with the ray to the right.

Question 2 Negative Coefficient (2 points)

Subtract 7: −3x < −15. Divide by −3 and reverse the sign: x > 5.

Scoring: 1 point for −3x < −15, 1 point for the reversed sign and 5.

Question 3 Decimal Inequality (2 points)

Add 1.6: 0.4x < 4. Divide by 0.4: x < 10.

Scoring: 1 point for each correct step.

Question 4 Negative Factor Outside (3 points)

1. Divide by −4 and reverse the sign: x + 2 > −5. Subtract 2: x > −7.
2. Dividing both sides by a negative number reverses their order, so < becomes >.

Scoring: part a, 1 point for the division with the reversed sign and 1 point for the final answer; part b, 1 point.

Question 5 Fraction and Negative (3 points)

Add 2: −34x > 6. Multiply by −43 and reverse the sign: x < −8.

Test −12: −34(−12) − 2 = 9 − 2 = 7, and 7 > 4.

x < −8

Scoring: 1 point for adding 2, 1 point for the reciprocal step, 1 point for the reversed sign and result.

Question 6 Transit Card (3 points)

1. 85 − 2.75r > 30.
2. Subtract 85: −2.75r > −55. Divide by −2.75 and reverse the sign: r < 20.
3. The rides are whole numbers below 20, so 19 rides. Check: 85 − 2.75(19) = 32.75.

Scoring: 1 point per part.

Question 7 Reading a Graph (3 points)

1. x > −2.
2. No. The circle is open, so −2 is not included, and 3(−2) + 4 = −2 is not greater than −2.
3. Subtract 4: 3x > −6. Divide by 3: x > −2, which matches.

Scoring: 1 point per part.

Question 8 Find the Mistake (2 points)

1. Kai divided both sides by −6 but did not reverse the inequality sign.
2. Subtract 5: −6x > 24. Divide by −6 and reverse the sign: x < −4. Test −5: −6(−5) + 5 = 35 > 29.

Scoring: 1 point per part.