Identifying Properties When Solving Equations

While solving the equation 4(x + 2) = 28, Becca

wrote 4x + 8 = 28. Which property did she use?

• associative property

• commutative property

• distributive property

• zero property of addition

When solving the equation 4(3x² + 2) − 9 = 8x² + 7,

Emily wrote 4(3x² + 2) = 8x² + 16 as her first step.

Which property justifies Emily's first step?

• addition property of equality

• commutative property of addition

• multiplication property of equality

• distributive property of multiplication over

  addition

A part of Jennifer's work to solve the equation

2(6x² − 3) = 11x² − x is shown below.

Given: 2(6x² − 3) = 11x²− x

Step 1: 12x² − 6 = 11x² − x

Which property justifies her first step?

• identity property of multiplication

• multiplication property of equality

• commutative property of multiplication

• distributive property of multiplication over

  subtraction

When solving the equation

12x² − 7x = 6 − 2(x² − 1), Evan wrote

12x² − 7x = 6 − 2x² + 2 as his first step. Which

property justifies this step?

• subtraction property of equality

• multiplication property of equality

• associative property of multiplication

• distributive property of multiplication over

  subtraction

When solving for the value of x in the equation

4(x − 1) + 3 = 18, Aaron wrote the following lines

on the board.

[line 1] 4(x − 1) + 3 = 18

[line 2] 4(x − 1) = 15

[line 3] 4x − 1 = 15

[line 4] 4x = 16

[line 5] x = 4

Which property was used incorrectly when going

from line 2 to line 3?

• distributive

• commutative

• associative

• multiplicative inverse

Britney is solving a quadratic equation. Her first

step is shown below.

Problem: 3x² − 8 − 10x = 3(2x + 3)

Step 1: 3x² − 10x − 8 = 6x + 9

Which two properties did Britney use to get to step

1?

I. addition property of equality

II. commutative property of addition

III. multiplication property of equality

IV. distributive property of multiplication

over addition

• I and III

• I and IV

• II and III

• II and IV

Which statement best illustrates the additive identity property?

• 6+2=2+6

• 6(2)=2(6)

• 6+(-6)=0

• 6+0=6

Which equation illustrates the associative property?

• x + y + z

• x(y + z)=xy + xz

• x + y + z=z + y + x

• (x + y) +z =x + (y +z)

Which equation illustrates the distributive property for real numbers?

• (1.3 x 0.07) x0.63=1.3 x (0.07 x 0.63)

• -3(5 + 7)=(-3)(5) + (-3)(7)

Which is an illustration of the additive identity property?

• x +0=x

• x-x=0