Solving Linear Equations: Distributive Property Answers

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?

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

✔ combine like termsdistributive propertydivision property of equalitysubtraction property of equality

combine like termsdistributive propertydivision property of equality✔ subtraction property of equality

Step 4:[___]

Step 5:[___]

n = [___]

Use the equation solver to find the value of x that makes the mathematical statement true.

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

Which equation is an identity?

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?

Which best describes Nosaira’s work and answer?

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.

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Which equation is an identity?

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?

Which best describes Nosaira’s work and answer?

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?