Number operations and properties (1-6 jmap questions)

1.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

2. A part of Jahsir'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

3. When solving the equation 12x² -7x=6 -2(x²-1), Elijah 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 subtractions

4. Breona 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 Breona 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

5. When solving p² +5 = 8p -7 Carnessa wrote p² + 12 = 8p. The property she used is

• the associative property

• the commutative property

• the distributive property

• the addition property of equality

6. A student is in the process of solving an equation. The original equation and the first step are shown below.

Original: 3a + 6 = 2 -5a +7

Step 1: 3a +6 = 2 + 7 -5a

Which property did the student use for the first step? Explain why this property is correct.

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