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Math 7

Math 7 · Worksheets

Mixed review · Patterns and equations

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

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Mixed review · Patterns and equations

Math 7 · maddyhelps.com

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

  1. Which expression means 'seven less than three times a number n'?

    1. a) 7 − 3n
    2. b) 3(n − 7)
    3. c) 3n + 7
    4. d) 3n − 7

  2. A pan balance shows 3x + 2 = 14. Everything on both pans is doubled. Which equation shows the new balance?

    1. a) 3x + 2 = 28
    2. b) 6x + 2 = 28
    3. c) 6x + 4 = 28
    4. d) 6x + 4 = 14

  3. Evaluate n/4 + 5 when n = 12.

    1. a) 17
    2. b) 53
    3. c) 8
    4. d) 4.25

  4. Solve x/4 = 6.

    1. a) x = 24
    2. b) x = 2
    3. c) x = 10
    4. d) x = 1.5

  5. 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) 3c + 4 = 23
    2. b) 4c + 3 = 23
    3. c) c + 3 = 23
    4. d) 7c = 23

  6. Evaluate 4n − 3 when n = 5.

    1. a) 17
    2. b) 8
    3. c) 42
    4. d) 6

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

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

  8. Which statement about 2x + 5 and 2x + 5 = 17 is true?

    1. a) The first is an expression; the second is an equation with one solution.
    2. b) Both are expressions, because neither one gives a value for x.
    3. c) Both are equations, because both of them contain the variable x.
    4. d) The first can be solved for x; the second can only be evaluated.

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

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

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

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

Answer key · Mixed review · Patterns and equations

Math 7 · maddyhelps.com

  1. d) 3n − 7 — Three times the number is 3n, and seven less than that takes 7 away from it: 3n − 7. Writing 7 − 3n follows the order of the words, but 'seven less than' means take 7 away from the other amount — just as 7 less than 10 is 10 − 7 = 3.
  2. c) 6x + 4 = 28 — Doubling everything means the 3 bags become 6, the 2 becomes 4 and the 14 becomes 28: 6x + 4 = 28. Doubling the bags but not the 2 gives 6x + 2 = 28, which is false for the solution, x = 4: 6 × 4 + 2 = 26, not 28.
  3. c) 8 — Divide first: 12 ÷ 4 = 3, then add 5 to get 8. 53 multiplies by 4 instead of dividing, and 4.25 adds before dividing, (12 + 5) ÷ 4 — but here the 4 divides only the n.
  4. a) x = 24 — x divided by 4 gives 6, so undo the division by multiplying both sides by 4: x = 24. Check: 24 ÷ 4 = 6 ✓. Dividing 6 by 4 gives 1.5, which divides again instead of undoing the division.
  5. b) 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.
  6. a) 17 — 4n means 4 × n, so 4 × 5 − 3 = 20 − 3 = 17. Writing the 5 next to the 4 gives 45 − 3 = 42; the variable stands for a number that is multiplied by 4, not a missing digit.
  7. c) 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.
  8. a) The first is an expression; the second is an equation with one solution. — 2x + 5 has no equal sign, so it is an expression, with a value for any x you choose — 7 when x = 1, 15 when x = 5. Adding = 17 makes an equation, which is true only when x = 6. A variable does not make something an equation; the equal sign does.
  9. d) 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.
  10. 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.