SOLVING EQUATIONS USING DISTRIBUTIVE PROPERTY

SOLVING EQUATIONS USING DISTRIBUTIVE PROPERTY

by Alecia Harris

By the end of this lesson you will be able to solve linear equations that require distribution

Steps:

• Distribute wherever there are parantheses

• Combine like terms on each side of the equation

• Inverse Operations to solve for the variable

• Check your work

Example: Solve the equation

4(3x - 5) = 52

Step 1: Distribute wherever necessary

4(3x - 5) = 52

Steps:

• distribute
• solve using inverse operations
• check your work

Step 2: Solve Using Inverse Operations

12x - 20 = 52

12x = 72
x = 6

-  Add 20 to both sides

- Divide both sides by 12

Step 3: Check x = 6

4 (3*6 - 5 ) = 52

4(18 - 5) = 52

4(13) = 52

52 = 52 CHECKS!

Multiple Choice

Distribute:

4(x+2)

• 4x+8

• 4x+2

• $$\frac{x+2}{4}$$

• 8x

Multiple Choice

Distribute:

2(b-3)

• -6b

• 6b

• 2b-6

• 2b-3

Multiple Choice

Distribute:

-2(x+1)

• -2x

• -2x+1

• -2x+2

• -2x-2

Multiple Choice

What is the first step in solving this equation?

2(x+2) = 3x + 4

• Distribute the 2 and the (x+2)

• Divide both sides by 2

• Subtract 4 from each side

• Do the hokey pokey

Multiple Choice

Solve:

2(x+1) = 6

• x = -1

• x = 4

• x = 2

• x = -2

Multiple Choice

Solve:

-2(x-1) = 6

• x = 2

• x = -2

• x = 4

• x = -4

Multiple Choice

How do you know when you need to distribute?

• You never have to distribute

• There is an equal sign

• There are exponents

• There are parenthesis

Multiple Choice

4( x + 2) = 16

What is the solution to the equation?

• -2

• 0

• 1

• 2

Multiple Choice

3(x+1)=9

• 2
• 8/3
• 5
• 4

Multiple Choice

5(x+5)=30

• 7
• 5
• 1
• 6

Multiple Choice

5(x-3)=40

• 11
• 43/5
• 38
• 37/5