Solving Linear Equations: Distributive Property

Question 1

Which of these equations have no solution? Check all that apply.2(x + 2) + 2 = 2(x + 3) + 12x + 3(x + 5) = 5(x – 3)4(x + 3) = x + 124 – (2x + 5) = (–4x – 2)5(x + 4) – x = 4(x + 5) – 1

Revolt · Accepted Answer

A: 2(x + 2) + 2 = 2(x + 3) + 1; B: 2x + 3(x + 5) = 5(x – 3); E: 5(x + 4) – x = 4(x + 5) – 1

Question 2

Which equation is an identity?

Revolt · Accepted Answer

C: 2x + 3 = (4x + 2) + 2

Question 3

To babysit one child, Fernando charges $10 to drive to the appointment plus $4 per hour. He saves 30% of the total amount he earns. Brenna charges $6 per hour and saves 25% of the total amount she earns. Which equation can be used to determine the number of hours, h, after which Fernando and Brenna will have saved the same amount of money?

Revolt · Accepted Answer

C: 0.3(10 + 4h) = 0.25(6h)

Question 4

Which best describes Nosaira’s work and answer?

Revolt · Accepted Answer

A: Her work is correct, but there is one solution rather than no solution.

Question 5

Leena consumes 400 calories at breakfast and 350 calories at lunch. She consumes of her daily calories at dinner. If x represents the calories consumed at dinner, which statements describe the situation? Check all that apply.Leena consumed 1,500 calories at dinner.The equation (x + 400 + 350) = x can be used to model the situation.Leena consumed 500 calories at dinner. The equation (x) = x(400 + 300) can be used to model the situation.Leena consumed 1,000 calories at dinner. The equation x(400 + 300) = x can be used to model the situation.

Revolt · Accepted Answer

A: Leena consumed 1,500 calories at dinner.; B: The equation (x + 400 + 350) = x can be used to model the situation.

Question 6

⇒ 10

Revolt · Accepted Answer

72384

Question 7

Markus scored 85, 92, 82, and 94 on the first four tests of the semester. His teacher has not yet told him his score on his fifth test, but did tell him that his score on the fifth test is five points lower than the average (arithmetic mean) of all five tests. Which equation could Markus use to determine the score of the fifth test, x?

Revolt · Accepted Answer

B: 5(x + 5) = 353 + x

Question 8

Use the drops-downs to justify how Heidi arrived at each step.

Revolt · Accepted Answer

Step 1:: distributive property; Step 2:: combine like terms; Step 3:: subtraction property of equality; Step 4:: addition property of equality; Step 5:: division property of equality

Question 9

Use the drops-downs to justify how Heidi arrived at each step.

Revolt · Accepted Answer

C: ✔ distributive property

Question 10

✔ combine like termsdistributive propertydivision property of equalitysubtraction property of equality

Revolt · Accepted Answer

A: ✔ combine like terms

Solving Linear Equations: Distributive Property Answers

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