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Grade 9 · Math · Algebra 1

9th grade Name the property, and give the reason for each step in solving an equation worksheet

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Name the property, and give the reason for each step in solving an equation

Grade 9 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

  1. Read this first

    Line A

    2(3x − 4) = 4x + 10. Line B: 6x − 4 = 4x + 10. Line C: 2x − 4 = 10. Line D: 2x = 14. Line E: x = 7.

  2. Luz solves 2(3x − 4) = 4x + 10 and gets x = 7. Which line, A to E, is the first one that is wrong?

  3. Line A

    3(2x − 1) + 4 = 5x + 12. Line B: 6x − 3 + 4 = 5x + 12. Line C: 6x − 1 = 5x + 12. Line D: x − 1 = 12. Line E: x = 13.

  4. Milo solves 3(2x − 1) + 4 = 5x + 12 and gets x = 13. Which line, A to E, is the first one that is wrong?

  5. Line A

    x/3 + x/6 = 9. Line B: 2x/6 + x/6 = 9. Line C: 3x/12 = 9. Line D: x/4 = 9. Line E: x = 36.

  6. Pia solves x/3 + x/6 = 9 and gets x = 36. Which line, A to E, is the first one that is wrong?

  7. Jun rewrites 3(x + 4) − 2(x + 4) as (3 − 2)(x + 4). What is the reason for this rewrite?

    • Associative property of addition
    • Commutative property of multiplication
    • Distributive property
    • Subtraction property of equality

  8. Ren rewrites (x + 3) + (−(x + 3)) as 0. What is the reason for this rewrite?

    • Distributive property
    • Inverse property of addition
    • Addition property of equality
    • Identity property of addition

  9. Pia rewrites x · (1/x), for x not 0, as 1. What is the reason for this rewrite?

    • Inverse property of multiplication
    • Identity property of multiplication
    • Distributive property
    • Multiplication property of equality

  10. Bo wants the x terms together in 7x − 2 = 3x + 10. Which move keeps the equation true?

    • Add 3x to both sides: 10x − 2 = 6x + 10
    • Subtract 3x from the left side alone: 4x − 2 = 3x + 10
    • Subtract 3x from the left, add 3x to the right: 4x − 2 = 6x + 10
    • Subtract 3x from both sides: 4x − 2 = 10

  11. Esme wants the x terms together in −2x + 9 = 5 − 3x. Which move keeps the equation true?

    • Add 3x on the left, subtract 3x on the right: x + 9 = 5 − 6x
    • Add 3x to the left side alone: x + 9 = 5 − 3x
    • Subtract 3x from both sides: −5x + 9 = 5 − 6x
    • Add 3x to both sides: x + 9 = 5

  12. Kira wants the x alone in (2/5)x = 6. Which move keeps the equation true?

    • Multiply just the left side by 5/2: x = 6
    • Multiply both sides by 2/5: (4/25)x = 12/5
    • Multiply the left by 5/2 and the right by 2/5: x = 12/5
    • Multiply both sides by 5/2: x = 15

  13. Luz wants to clear the fractions in x/3 + 2 = x/2. Which move keeps the equation true?

    • Multiply just the left side by 6: 2x + 12 = x/2
    • Multiply both sides by 6: 2x + 12 = 3x
    • Multiply the left by 6 and divide the right by 6: 2x + 12 = x/12
    • Divide both sides by 6: x/18 + 1/3 = x/12
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9th grade Name the property, and give the reason for each step in solving an equation worksheet – printable
Print: 123456

About this worksheet

Name the property, and give the reason for each step in solving an equation. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can name the property that makes a rewrite true (for example, commutative or distributive).
  • I can give the reason for a step in solving an equation: do the same thing to both sides.
  • I can find the first line with a mistake in a worked solution.

Standard: A-REI.A.1 (A-SSE.A.2 supports)

Words to know

property: A rule that is always true for numbers, such as swapping the order of an addition.

commutative: Two pieces trade places and the total stays the same.

associative: The pieces keep their order and only the brackets move.

identity: Adding 0 or multiplying by 1 leaves the number the same.

inverse: A number and its opposite make 0 (or a number and its flip make 1).

property of equality: Do the same thing to both sides and the equation stays true.

Common mistakes

Your child mixed up swapping the order with regrouping.

Your child mixed up the property that keeps a number the same with the one that makes 0 or 1.

Your child named the operation that is in the equation, but the step undoes it.

What to say

Ask: in this step, did the numbers trade places or did the brackets move?

Ask: does the number stay the same, or does it become 0 or 1?

Ask: what was done to both sides to get the letter alone?

Questions parents ask

What is the most common mistake with name the property, and give the reason for each step in solving an equation?

Your child mixed up swapping the order with regrouping.

How can I help my child with name the property, and give the reason for each step in solving an equation?

Ask: in this step, did the numbers trade places or did the brackets move?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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