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

Answer Key - Grade 9 Math Worksheet

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

1. Read this first

   Line 1

   3x − 4 = 5 − (x − 7). Line 2: 3x − 4 = 12 − x. Line 3: 4x − 4 = 12. Line 4: x − 1 = 3. Line 5: x = 4.

2. 1.

   Milo solves 3x − 4 = 5 − (x − 7) in five lines. What is the reason for going from line 2 to line 3?

   • Subtraction property of equality
   • Distributive property
   • Addition property of equality
   • Division property of equality
3. 2.

   x/2 + x/3 = 10. Line 2: (5/6)x = 10. Line 3: x = 12. Noah solves x/2 + x/3 = 10 in three lines. What is the reason for going from line 1 to line 2?

   • Distributive property, which combines like terms
   • Addition property of equality
   • Multiplication property of equality
   • Commutative property of addition

4. Line 1

   2x − 3 = 5x + 9. Line 2: −3 = 3x + 9. Line 3: −12 = 3x. Line 4: −4 = x.

5. 3.

   Pia solves 2x − 3 = 5x + 9 in four lines. What is the reason for going from line 1 to line 2?

   • Distributive property
   • Division property of equality
   • Subtraction property of equality
   • Addition property of equality
6. 4.

   Ren rewrites (3x)(4) as 12x. Which properties of numbers allow this?

   • Distributive property
   • Just the associative property of multiplication
   • Commutative and associative properties of multiplication
   • Just the commutative property of multiplication
7. 5.

   Tala rewrites 3x + 12 as 3(x + 4). Which property of numbers allows this?

   • Commutative property of multiplication
   • Distributive property
   • Identity property of multiplication
   • Associative property of multiplication
8. 6.

   Zee solves (x − 3)(x + 4) = 0 and writes x − 3 = 0 or x + 4 = 0. Which property allows this?

   • Distributive property
   • Multiplication property of equality
   • Zero-product property
   • Identity property of multiplication
9. 7.

   Ari rewrites 12 = 3x as 3x = 12. Which property of equality allows this?

   • Transitive property of equality
   • Commutative property of multiplication
   • Symmetric property of equality
   • Reflexive property of equality
10. 8.

    Esme has 3(x + 4) = 27 and divides both sides by 3. The left side becomes x + 4. What does the right side become?

    9
11. 9.

    Luz has x/5 − 3 = 4 and adds 3 to both sides. The left side becomes x/5. What does the right side become?

    7
12. 10.

    Noah has −2x + 7 = 15 and subtracts 7 from both sides. The left side becomes −2x. What does the right side become?

    8