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Grade 7 · Math · Unit 10 of 16

Two-Step Equations

Undo, undo, solve for x

What your child practises

Solving equations like 3x + 5 = 26 by undoing each step on both sides, writing equations from word problems and checking solutions.

Alberta Curriculum learning outcome: PR7 · solving linear equations of the form ax + b = c

How we explain it

Children can open this short lesson before they practise.

  1. Keep the equation balanced: do the same to both sides.
  2. Undo the adding or subtracting first.
  3. Then undo the multiplying or dividing.

Example: 2x + 3 = 11 Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Answer: x = 4

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    On a balance scale, 2 identical bags of marbles plus 15 loose marbles balance 23 loose marbles. How many marbles are in each bag?

    ⚖️2x + 15 = 23

    answer box

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    4

    Hint: Take 15 marbles off both sides: 2 bags balance 8 marbles. Share them among 2 bags: 8 ÷ 2 = 4.

  2. Question 2

    Which equation matches this sentence? "Two times a number, minus 3, equals 9."

    • 2(n − 3) = 9
    • 2n + 3 = 9
    • 2n − 3 = 9
    • 3n − 2 = 9
    Show answer

    2n − 3 = 9

    Hint: "Two times a number" is 2n. "Minus 3" subtracts 3 after multiplying: 2n − 3. "Equals 9" finishes it: 2n − 3 = 9.

  3. Question 3

    Solve for x.

    55 = 7x − 8

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    9

    Hint: The x can be on either side. Add 8 on both sides: 63 = 7x. Then divide by 7: x = 9.

  4. Question 4

    A rectangle has a perimeter of 114 cm and a width of 18 cm. What is its length?

    answer boxcm

    Show answer

    39 cm

    Hint: Perimeter = 2L + 2w, so 2L + 36 = 114. Subtract 36: 2L = 78. Divide by 2: L = 39 cm.

  5. Question 5

    Solve for x.

    5x + 11 = 86

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    15

    Hint: Undo the + 11 first: subtract 11 from both sides to get 5x = 75. Then undo the × 5: divide both sides by 5 to get x = 15.

  6. Question 6

    Is x = 3 a solution of 6x − 11 = 1?

    6x − 11 = 1

    • Yes
    • No
    Show answer

    No

    Hint: Substitute x = 3: 6 × 3 − 11 = 7. That isn't 1, so x = 3 is not a solution.

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