Writing Algebraic Equations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Writing algebraic equations

Mathematics · Algebra · ages 10-11
Name ______________________   Date ____________

  1. I think of a number, multiply it by 4, and subtract 2. The answer is 18. Which equation matches this story?

    • 4n - 2 = 18
    • n - 2 = 18
    • 4(n - 2) = 18
    • 4n = 18 - 2

  2. Which equation matches 'I think of a number and add 5 to get 12'?

    • 5n = 12
    • n + 5 = 12
    • n - 5 = 12

  3. In algebra, a letter like n can stand for a number we don't know yet.

    Circle one:   True   False

  4. In the equation 3x = 24, what does x stand for?

    • The number 3
    • The number 24
    • The unknown number

  5. Two numbers add up to 20. One of the numbers is 9. Write the equation n + 9 = 20 and find the other number.

    Answer: ______________

  6. To solve 5x = 45, you divide both sides by 5, and the answer is x = 9.

    Circle one:   True   False

  7. Sam had some marbles. He gave 6 to his friend and now has 9 left. Which equation finds how many marbles Sam started with?

    • n + 6 = 9
    • n - 6 = 9
    • 6n = 9
    • n - 9 = 6

  8. A number is multiplied by 5, then 3 is taken away, and the result is 22. First write this as the equation 5n - 3 = 22, then solve it. What is the number?

    Answer: ______________

  9. Leo solved 4x = 28 and wrote x = 24. What mistake did Leo make?

    • He subtracted 4 instead of dividing by 4
    • He divided by the wrong number
    • He added 4 to both sides

  10. A number is tripled, then 6 is subtracted, and the result is 15. What is the number?

    Answer: ______________

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Answer key

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Writing algebraic equations W1-mt_i9rJbuFO3p-s1

  1. 4n - 2 = 18 · Multiplying the number by 4 gives 4n, subtracting 2 gives 4n - 2, and the answer 18 goes on the other side of the equals sign.
  2. n + 5 = 12 · The number n has 5 added to it, so the equation is n + 5 = 12.
  3. True · That is exactly what a variable does: it holds the place of an unknown number.
  4. The unknown number · x is the letter that holds the place of the number you still need to find.
  5. 11 · The sum becomes n + 9 = 20. Subtracting 9 from both sides gives n = 11, and 11 + 9 really is 20.
  6. True · Dividing both sides by 5 undoes the multiplication, and 45 divided by 5 really is 9, so the statement is true.
  7. n - 6 = 9 · He started with n, gave away 6, so n - 6, and that equals 9. Solving gives n = 15.
  8. 5 · The story becomes 5n - 3 = 22. Adding 3 to both sides gives 5n = 25, and dividing by 5 gives n = 5.
  9. He subtracted 4 instead of dividing by 4 · Multiplication is undone by dividing, not subtracting: x = 28 ÷ 4 = 7.
  10. 7 · The equation is 3n - 6 = 15. Add 6 to both sides: 3n = 21. Divide by 3: n = 7.
Worksheet · LightMySky