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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a two-step equations test answer key? Then this answer key gives the solutions and the scoring guide of the Grade 7 test on Solving Two-Step Equations with Rational Numbers. Award points as marked. Give full credit for any correct method, such as distributing first or dividing first, and allow one point of partial credit when a single arithmetic slip is followed correctly through the remaining steps.
Standards: 7.EE.B.3, 7.EE.B.4a · Level: Grade 7
Question 1 Solve Two Equations (2 points)
- 6x = 42, so x = 7.
- 4x = −24, so x = −6.
Scoring: 1 point per part.
Question 2 A Quotient Equation (2 points)
Add 8: x5 = 5. Multiply by 5: x = 25. Check: 25 ÷ 5 − 8 = −3.
Scoring: 1 point for each correct step.
Question 3 Decimal Coefficients (2 points)
Subtract 1.6: 3.2x = 12.8. Divide by 3.2: x = 4. Check: 3.2(4) + 1.6 = 14.4.
Scoring: 1 point for each correct step.
Question 4 Two Ways with Parentheses (3 points)
- x − 2.4 = 3.2, so x = 5.6.
- 5x − 12 = 16, so 5x = 28 and x = 5.6.
- 5(5.6 − 2.4) = 5(3.2) = 16. x = 5.6.
Scoring: 1 point per part.
Question 5 Fractions in an Equation (3 points)
Multiply by 43: x + 23 = 143. Subtract 23: x = 123 = 4.
Check: 34 · 143 = 144 = 72.
Scoring: 1 point for the reciprocal step, 1 point for the subtraction, 1 point for the result.
Question 6 Equation from a Diagram (3 points)
- 3x + 7.5 = 31.5.
- 3x = 24, so x = 8.
- 3(8) + 7.5 = 24 + 7.5 = 31.5.
Scoring: 1 point per part.
Question 7 Gym Membership (3 points)
- 18.50m + 35 = 146.
- 18.50m = 111, so m = 6.
- Nia has been a member for 6 months. Check: 18.50(6) + 35 = 111 + 35 = 146.
Scoring: 1 point per part.
Question 8 Find the Mistake (2 points)
- On line 2 he multiplied 18 by 2; the factor 2 should be divided out, not multiplied.
- Divide by 2: x + 5 = 9, so x = 4. Check: 2(4 + 5) = 18.
Scoring: 1 point per part.