Solving Linear Equations: Distributive Property: Assignment

Which of these equations have no solution? Check all that apply.

1. 2(x + 2) + 2 = 2(x + 3) + 1 2. 2x + 3(x + 5) = 5(x - 3) 5. 5(x + 4) - x = 4(x + 5) - 1

What is the value of n in the equation -1/2(2n+4)+6=-9+4(2n+1)

n=1

6.8x+9.3=-9.4x+3.4(2-5x)

A. -0.5

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.

1. Leena consumed 1,500 calories at dinner. 2. The equation 2/3(x + 400 + 350) = x can be used to model the situation.

Heidi solved the equation3(x + 4) + 2 = 2 + 5(x - 4). Her steps are below: 3x + 12 + 2 = 2 + 5x - 20 3x + 14 = 5x - 18 14 = 2x - 18 32 = 2x 16 = x Step 1: Step 2: Step 3: Step 4: Step 5:

1. distributive property 2. combine like terms 3. subtraction property of equality 4. addition property of equality 5. division property of equality

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?

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

Nosaira solved an equation. Her work is shown below: 3(2x + 1 ) = 2(x + 1) + 1 6x + 3 = 2x + 2 + 1 6x + 3 = 2x + 3 4x = 0 x = 0 She determines the equation has no solution. Which best describes Nosaira's work and answer?

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

The congruent sides of an isosceles triangle are each 1 unit longer than the length of the shortest side of the triangle. The perimeter of the triangle is the same as the perimeter of a square whose side length is 2 units shorter than the length of the shortest side of the triangle. What is the length of the shortest side of the triangle?

10 units

Which equation is an identity?

C. 2x + 3 = 1/2(4x + 2) + 2

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?

C. 5(x + 5) = 353 + x