Testinar Grade 7 math

Solving Multi-Step Problems with Rational Numbers

Students will build Grade 7 mastery of solving multi-step problems with rational numbers using models, equations, and test-style reasoning.

CH05-04 Equations and Inequalities
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Solve: \(\frac{1}{2}x-3=5\) and check that your answer is reasonable.

    1. \(x=6\)
    2. \(x=10\)
    3. \(x=16\)
    4. \(x=24\)

  2. Solve \(3x+7=22\) and explain why your answer is reasonable.

    1. \(x=5\)
    2. \(x=9.67\)
    3. \(x=10\)
    4. \(x=15\)

  3. Solve for \(y\): \(2y-8=-14\) and check your answer makes sense.

    1. \(y=-3\)
    2. \(y=0\)
    3. \(y=3\)
    4. \(y=11\)

  4. Which value of \(x\) satisfies \(\frac{x}{4}+2=5\)? Use mental math to verify.

    1. \(x=6\)
    2. \(x=12\)
    3. \(x=20\)
    4. \(x=28\)

  5. Solve: \(5(x-2)=30\) and verify using inverse operations.

    1. \(x=6\)
    2. \(x=8\)
    3. \(x=10\)
    4. \(x=12\)

  6. A savings account has a balance of \(-$15\) (overdraft). After depositing $50, what is the new balance? Write and solve an equation.

    1. \($25\)
    2. \($35\)
    3. \($50\)
    4. \($65\)

  7. Marcus earns $12 per hour. After working 8 hours, he spent $15 on lunch. How much money does he have left?

    1. \($81\)
    2. \($96\)
    3. \($111\)
    4. \($127\)

  8. What is the solution to \(\frac{3}{4}x=12\)? Use a reciprocal to solve and verify.

    1. \(x=9\)
    2. \(x=12\)
    3. \(x=16\)
    4. \(x=36\)
Teacher and parent reference

Answer key and explanations

  1. C. \(x=16\)

    Add \(3\) to both sides: \(\frac{1}{2}x=8\). Multiply by \(2\): \(x=16\). Check: \(\frac{1}{2}(16)-3 = 8-3 = 5\) ✓. Reasonableness: Half of 16 is 8; minus 3 gives 5. ✓

  2. A. \(x=5\)

    Subtract \(7\): \(3x=15\). Divide by \(3\): \(x=5\). Check: \(3(5)+7 = 15+7 = 22\) ✓. Reasonable: three times 5 is 15; add 7 gives 22.

  3. A. \(y=-3\)

    Add \(8\): \(2y=-6\). Divide by \(2\): \(y=-3\). Check: \(2(-3)-8 = -6-8 = -14\) ✓. Reasonable: negative answer expected (result is negative).

  4. B. \(x=12\)

    Subtract \(2\): \(\frac{x}{4}=3\). Multiply by \(4\): \(x=12\). Mental math check: \(\frac{12}{4}+2 = 3+2 = 5\) ✓. Reasonable: one-quarter of 12 is 3; add 2 gives 5.

  5. B. \(x=8\)

    Divide by \(5\): \(x-2=6\). Add \(2\): \(x=8\). Check: \(5(8-2) = 5(6) = 30\) ✓. Reasonable: five groups of 6 equals 30.

  6. B. \($35\)

    Equation: \(-15 + d = b\) where \(d = 50\) (deposit). Or: \(-15 + 50 = 35\). Check: Starting with \(-$15\) debt, adding \($50\) leaves \($35\) surplus. Reasonable.

  7. A. \($81\)

    Earnings: \(12 \times 8 = 96\). After spending: \(96 - 15 = 81\).

  8. C. \(x=16\)

    Multiply both sides by \(\frac{4}{3}\) (reciprocal): \(x = 12 \times \frac{4}{3} = 16\). Check: \(\frac{3}{4}(16) = \frac{3 \times 16}{4} = \frac{48}{4} = 12\) ✓. Reasonable: three-quarters of 16 is 12.

Free Testinar sample Reviewed November 6, 2026 testinar.com
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