Solving with the Distributive Property Assignment

Emma wants to use the distributive property to solve this equation. 5(x - 2) = 30 Help her follow these steps to finish solving for x. 1. Distributive property: 5x - 10 = 30 2. Addition property of equality: 5x = 40 3. Division property of equality: x = 8

8

Callie solved this one-variable equation. When she was done, she tried to verify her answer, but found that it was wrong. Can you find her mistake? 1 2 (4k + 8) = 10 1. 2k + 16 = 10 2. 2k = −6 3. k = −3 What was Callie's mistake?

B.In step 1, when Callie distributed the mc001-1.jpg to the 8, she multiplied incorrectly.

Solve the one-variable equation using the distributive property and properties of equality. -6(2 + a) = -48 What is the value of a?

D

Generate a plan and describe the steps needed to solve the equation. 34 = -(m + 3)

The negative sign outside the parentheses represents -1. Distribute the -1 to everything inside the parenthesis. Use the addition property of equality first to add 3 to both sides. Then use the division property of equality to divide both sides by -1.

The diagram below represents the measurements of Jennie's yard. The yard's width is x feet shorter than its length. If the area of the yard is 540 square feet, how many feet shorter than the length is the width? rectangle Solve the equation to find how many feet shorter than the length the width is. 30(30 - x) = 540 What is the value for x?

12

Labron makes $100 per week and takes no vacation during the entire year. His friend, Jordan, makes $4800 per year at the same weekly rate. Jordan takes x vacation weeks per year. Note: There are 52 weeks in a year. This equation represents how to find Jordan's number of vacation weeks. 100(52 - x) = 4800 Labron says that Jordan takes 4 weeks of vacation each year. Is he correct? Check all that apply.

a

he diagram below represents the measurements of Jennie's yard. The yard's width is x feet shorter than its length. If the area of the yard is 540 square feet, how many feet shorter than the length is the width? rectangle Which equation represents the scenario?

c

The linear equation was solved using these steps. Linear equation: 1 3 (12x + 15) = 7 Step 1: 4x + 5 = 7 Step 2: 4x = 2 Step 3: x = 1 2 The property that was used in step 1 was the . The property that was used in step 2 was the . The property that was used in step 3 was the .

distributive property subtraction property of equality division property of equality

dentify the method that will be used to solve for x for each equation. 4x = 20

division property of equality addition property of equality combining like terms distributive property