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Solving Two-Step Equations: math test solutions, Grade 7 – download the PDF

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Test solutions Grade 7 : Solving Two-Step Equations — Zyro the alien explorer of Planète Maths

Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

1 Solve four equations / 4 pts

  1. \(3x = 21\), so \(x = 7\). (1 pt)
  2. \(\dfrac{x}{6} = 4\), so \(x = 24\). (1 pt)
  3. \(5x = 50\), so \(x = 10\). (1 pt)
  4. \(x + 9 = 20\), so \(x = 11\). (1 pt)

2 Checking values / 3 pts

  1. \(7(8) - 6 = 56 - 6 = 50\). Yes, it is a solution. (1 pt)
  2. \(2(-3) + 11 = 5\), and \(5 \neq 4\). No, it is not a solution. (1 pt)
  3. \(2x = -7\), so \(x = -3.5\). (1 pt)

3 Rational coefficients / 3 pts

  1. Subtract 2: \(\dfrac{3}{5}x = 9\). Multiply by \(\dfrac{5}{3}\): \(x = 15\). (1.5 pts)
  2. Add 1.2: \(0.4x = 3.2\). Divide by 0.4: \(x = 8\). (1.5 pts)

4 Saving for a bike / 4 pts

  1. \(7.5w + 12 = 57\). (1 pt)
  2. \(7.5w = 45\), so \(w = 6\). (2 pts)
  3. Nora reaches $57 after 6 weeks. Check: \(7.5(6) + 12 = 57\). (1 pt)

5 Garden fence / 3 pts

  1. \(2(x + 6) = 34\). (1 pt)
  2. \(x + 6 = 17\), so \(x = 11\). (1 pt) The garden is 11 m long. Check: \(2(11 + 6) = 34\). (1 pt)

6 Number puzzle / 3 pts

  1. Undo in reverse: \(53 - 9 = 44\), then \(44 \div 4 = 11\). (1.5 pts)
  2. \(4x + 9 = 53\), so \(4x = 44\) and \(x = 11\). (1.5 pts)
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