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

Answer Key - Grade 9 Math Worksheet - Challenge Me

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. 1.

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

   B

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. 2.

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

   C

5. Line A

   −3(x − 4) = 2x − 8. Line B: −3x − 12 = 2x − 8. Line C: −3x = 2x + 4. Line D: −5x = 4. Line E: x = −4/5.

6. 3.

   Noah solves −3(x − 4) = 2x − 8 and gets x = −4/5. Which line, A to E, is the first one that is wrong?

   B

7. 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.

8. 4.

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

   C
9. 5.

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

   • Distributive property
   • Multiplication property of equality
   • Inverse property of multiplication
   • Identity property of multiplication
10. 6.

    Tala knows x = 5 and 5 = y, and concludes x = y. What is the reason for this?

    • Addition property of equality
    • Reflexive property of equality
    • Symmetric property of equality
    • Transitive property of equality
11. 7.

    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 both sides: 4x − 2 = 10
    • Subtract 3x from the left, add 3x to the right: 4x − 2 = 6x + 10
12. 8.

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

    • Subtract 3x from both sides: −5x + 9 = 5 − 6x
    • Add 3x to the left side alone: x + 9 = 5 − 3x
    • Add 3x on the left, subtract 3x on the right: x + 9 = 5 − 6x
    • Add 3x to both sides: x + 9 = 5
13. 9.

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

    • Multiply both sides by 2/5: (4/25)x = 12/5
    • Multiply just the left side by 5/2: x = 6
    • Multiply both sides by 5/2: x = 15
    • Multiply the left by 5/2 and the right by 2/5: x = 12/5
14. 10.

    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 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
    • Multiply both sides by 6: 2x + 12 = 3x