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Math 7

Math 7 · Worksheets

Solving equations

Ten questions of mixed difficulty, covering Equations. Print it, or work through it on screen — the answer key starts on its own page.

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Solving equations

Math 7 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. Solve 5x + 4 = 39.

    1. a) x = 35
    2. b) x = 7
    3. c) x = 3.8
    4. d) x = 8.6

  2. Solve x − 8 = −3.

    1. a) x = −5
    2. b) x = −11
    3. c) x = 5
    4. d) x = 11

  3. Lina buys 4 identical notebooks and a $3 pen. She spends $23 in all. Which equation gives the cost, c, of one notebook?

    1. a) 4c + 3 = 23
    2. b) c + 3 = 23
    3. c) 7c = 23
    4. d) 3c + 4 = 23

  4. If 2x + 3 = 11, which equation must also be true?

    1. a) x + 3 = 11
    2. b) 2x = 8
    3. c) 2x = 14
    4. d) 2x + 3 = 8

  5. A music app charges a $10 sign-up fee plus $5 a month. Priya has paid $60 in all. How many months has she had the app?

    1. a) 12 months
    2. b) 6 months
    3. c) 10 months
    4. d) 14 months

  6. Solve x + 9 = 4.

    1. a) x = 13
    2. b) x = −5
    3. c) x = 5
    4. d) x = −13

  7. Which step gets x by itself in x + 7 = 12 and keeps the equation balanced?

    1. a) Subtract 7 from both sides.
    2. b) Subtract 7 from the left side only.
    3. c) Subtract 12 from both sides.
    4. d) Add 7 to both sides.

  8. On a pan balance, 3 identical bags of marbles balance 18 loose marbles. How many marbles are in each bag?

    1. a) 21
    2. b) 6
    3. c) 54
    4. d) 15

  9. Solve 6x + 5 = 8.

    1. a) x = 0.5
    2. b) x = 18
    3. c) x = 3
    4. d) x = 2

  10. Sam thinks of a number, n. When he adds 15 to it, he gets 42. Which equation fits?

    1. a) 15n = 42
    2. b) n + 42 = 15
    3. c) n − 15 = 42
    4. d) n + 15 = 42

Answer key · Solving equations

Math 7 · maddyhelps.com

  1. b) x = 7 — Subtract 4 from both sides to get 5x = 35, then divide both sides by 5: x = 7. Check: 5 × 7 + 4 = 39 ✓. Adding 4 instead gives 43 ÷ 5 = 8.6, and 35 stops before dividing by 5.
  2. c) x = 5 — Add 8 to both sides: x = −3 + 8 = 5. Check: 5 − 8 = −3 ✓. Subtracting 8 again gives −11, and the check fails: −11 − 8 = −19.
  3. a) 4c + 3 = 23 — Four notebooks cost 4c, and the pen adds $3 once: 4c + 3 = 23, so 4c = 20 and each notebook is $5. 3c + 4 swaps the number of notebooks with the price of the pen, and 7c = 23 treats the pen as three more notebooks.
  4. b) 2x = 8 — Subtracting 3 from both sides keeps the balance: 2x + 3 − 3 = 11 − 3, so 2x = 8. 2x = 14 adds 3 on the right while taking it away on the left, and 2x + 3 = 8 takes 3 away from the right side only.
  5. c) 10 months — The equation is 5m + 10 = 60. Take away the fee first, 5m = 50, so m = 10 — check: 5 × 10 + 10 = 60 ✓. 12 months ignores the fee (60 ÷ 5), and 14 adds the fee instead of taking it away.
  6. b) x = −5 — Subtract 9 from both sides: x = 4 − 9 = −5. Check: −5 + 9 = 4 ✓. Adding 9 instead gives 13, and 13 + 9 is 22, not 4.
  7. a) Subtract 7 from both sides. — Taking 7 away from both sides keeps the two sides equal and leaves x on its own: x = 5. Taking 7 from the left side only unbalances the equation. Adding 7 to both sides keeps it balanced but gives x + 14 = 19, which is further from x on its own.
  8. b) 6 — 3 bags balancing 18 marbles is the equation 3b = 18. Dividing both sides by 3 shares the 18 equally among the bags: b = 6. 15 subtracts the 3 instead of dividing, and 54 multiplies.
  9. a) x = 0.5 — Subtract 5 from both sides: 6x = 3. Then divide both sides by 6: x = 3 ÷ 6 = 0.5, and check: 6 × 0.5 + 5 = 8 ✓. Answering 2 divides 6 by 3, the wrong way round, to get a whole number — but an answer does not have to be a whole number.
  10. d) n + 15 = 42 — Adding 15 to n and getting 42 is n + 15 = 42, which gives n = 27. 15n = 42 multiplies instead of adding, and n − 15 = 42 takes 15 away, which would make the number 57.