Solving with the Distributive Property

Solving with the Distributive Property

Unit 2 Lesson 2

How to Solve an Equation using the Distributive Property

-6(2x - 5) = 6

Fill in the Blanks

Solve to find the value of x in the linear equation: 3(-4x+5)=12.

1. Use the Distributive Property: -12x + 15 = 12

2. Use the Subtraction Property of Equality: Subt. 15 from both sides: -12x = -3

3. Use the Division Property of Equality: Divide both sides by -12.

x =

Multiple Choice

Use the Distributive Property to solve for n:

3(-4n - 9) = 21

• -6

• -4

• 0.5

• 4

Identifying the Steps

Step 1:

Step 2:

Step 3:

Multiple Choice

Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?

• the addition property of equality and then the division property of equality

• the addition property of equality and then the multiplication property of equality

• the subtraction property of equality and then the division property of equality

• the subtraction property of equality and then the multiplication property of equality

Multiple Select

What steps might you take to verify the solution? Check all that apply.

• Substitute 7 for a.

• Pick any value for a and substitute.

• Simplify the equation after substituting the value for a.

• Verify that a = 7 is correct when the result is a true statement.

• Verify that a = 7 is correct when the result is a false statement.

Multiple Choice

Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. James makes $816 per year. How much less each month does James make than Matt?

Which expression represents the amount of money James makes each month?

• x - 12

• x - 80

• 80 - x

• 12 - x

Multiple Choice

Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. James makes $816 per year. How much less each month does James make than Matt?

Which equation represents the scenario?

• 12(80 - x) = 816

• 12(x - 80) = 816

• 80(12 - x) = 816

• 80(x - 12) = 816

Matt and James Lawn Mowing Business

12(80 - x) = 816

Distributive Property:

Subtraction Property of Equality

Division Property of Equality

Fill in the Blanks

How much does James earn each month? Remember that x represents how much LESS per month James makes than Matt.

Multiple Choice

What method will be used to solve for x in the equation 5(x - 2) = 30?

• Combining Like Terms

• Distributive Property

• Subtraction Property of Equality

• Multiplication Property of Equality

Fill in the Blanks

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 =

Multiple Choice

Solve the one-variable equation using the distributive property and properties of equality.

–6(2 + a) = –48

What is the value of a?

• -6

• -3

• 5

• 6

Multiple Choice

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

• Distributive Property

• Addition Property of Equality

• Subtraction Property of Equality

• Division Property of Equality

Multiple Choice

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? Which equation represents the scneario?

• 30 + (30 – x) = 540

• 540 – 30 = 30 – x

• 30(30 – x) = 540

• 540 – (30 – x) = 30

Multiple Choice

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?

• Yes, he is correct because substituting x = 4 into the equation yielded a true statement.

• Yes, he is correct because substituting x = 4 into the equation yielded a false statement.

• No, he is incorrect because substituting x = 4 into the equation yielded a true statement.

• No, he is incorrect because substituting x = 4 into the equation yielded a false statement.