Question

Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36

Given ⇒ 3(x − 4) + 5x = 9x − 36
Step 1 ⇒ 3x − 12 + 5x = 9x − 36
Step 2 ⇒ 3x + 5x − 12 = 9x − 36
Step 3 ⇒ 8x − 12 = 9x − 36
Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36
Step 5 ⇒ 0 − 12 = x − 36
Step 6 ⇒ −12 = x − 36
Step 7 ⇒ −12 + 36 = x − 36 + 36
Step 8 ⇒ 24 = x + 0
Step 9 ⇒ 24 = x

Which property yields Step 4?

Answer 1

A Subtraction Property of Equality
B Commutative Property of Addition
C Addition Property of Equality
D Additive Inverse Property

Answer 2

a

Answer 3

Given that x + y = 180, p + q = 180, and p = x. Show that y = q.

Which step would be used to prove the argument?

Answer 4

It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.
Responses
A associative
B commutative
C distributive
D identity

Answer 5

2(x + 7) + 3x = 12

What is the first step in solving this equation for x?

Answer 6

The property used in Step 4 is the property of combining like terms or simplifying expressions.

Answer 7

D Additive Inverse Property

Answer 8

The property used in Step 4 is the Addition Property of Equality.

Answer 9

To prove that y = q, we can substitute p = x into the equation p + q = 180. The appropriate step to prove the argument would be:

Substitute p = x into the equation p + q = 180 to get:

x + q = 180

Answer 10

C distributive

Answer 11

The first step in solving the equation 2(x + 7) + 3x = 12 is to simplify both sides of the equation by applying the distributive property.

The first step would be to distribute the 2 to the terms (x + 7):

2(x + 7) + 3x = 12
2x + 14 + 3x = 12