Lloyd solves the equation 24x+18(x-2)=216. Some of his steps are shown below.

Question

Step 1: 24x + 18(x-2)=216
Step 2: 24x+18x-36=216
Step 3: 42x-36=216
Step 4 : 42x=252

Which property BEST justifies what Lloyd did to get from Step 3 to Step 4?

Question 22 options:

Addition Property of Equality

Subtraction Property of Equality

Distributive Property

Division Property of Equality

Question 23 (1 point)

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Which property best describes how to get from step 3 to step 4 in the work below

8a-(15-a)=6(a-7)+15
Step 1: 8a-15+a=6a-42+15
Step 2: 9a-15=6a-27
Step 3: 3a-15=-24
Step 4: 3a=-12
Step 5: a =-4

Question 23 options:

Distributive Property

Division Property of Equality

Multiplication Property of Equality

Addition Property of Equality

Question 24 (1 point)

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Lloyd solves the equation 24x+18(x-2)=216. Some of his steps are shown below.

Which property should Lloyd use next to solve the equation for x?

Question 24 options:

Addition Property of Equality

Subtraction Property of Equality

Division Property of Equality

Distributive Property

Answer 1

Let's tackle each question one by one.

Question 22

Lloyd goes from Step 3: \( 42x - 36 = 216 \) to Step 4: \( 42x = 252 \).

To get this result, he added 36 to both sides of the equation. The property that justifies this operation is the Addition Property of Equality.

Answer for Question 22: Addition Property of Equality

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Question 23

In the equations provided, Lloyd transitions from Step 3: \( 3a - 15 = -24 \) to Step 4: \( 3a = -12 \).

To move from \( 3a - 15 = -24 \) to \( 3a = -12 \), Lloyd adds 15 to both sides of the equation. Therefore, the property used here is also the Addition Property of Equality.

Answer for Question 23: Addition Property of Equality

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Question 24

In this case, after Step 4, Lloyd has \( 42x = 252 \). To solve for \( x \), the next logical step is to isolate \( x \) by dividing both sides by 42. Thus, he should use the Division Property of Equality next.

Answer for Question 24: Division Property of Equality

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To summarize:

• Question 22: Addition Property of Equality
• Question 23: Addition Property of Equality
• Question 24: Division Property of Equality