Solve Multi-step Equations - Coppin Academy High School

[Pages:10]Solve Multi-step Equations

Students will solve equations with multiple steps (more than two) using distributive property, combining like

terms, and inverse operations.

REVIEW: Simplify Using the Distributive Property.

Distributive Property ? Multiply times everything in the parentheses. a ( b + c ) = ab + ac OR a ( b ? c ) = ab ? ac

Example 1: -3 ( x + 5 ) -3x ? 15

Example 2: -7 ( 2a ? 4 )

-14a + 28

REVIEW: Simplify Using Combining Like Terms

Like Terms must have the same variables and the same powers on the letters.

Combine like terms by adding or subtracting the coefficients (numbers in front of the variables).

Example 1: 3x + 5 ? 7x + 9

-4x + 14 Example 2: 3 ? 6y ? 7 ? 9y

-4 ? 15y

How do we simplify and solve equations with multiple steps?

To solve equations with multiple steps, first use the distributive property to get

rid of the parentheses.

Then, combine like terms to get the problem in the 2-step form.

Solve by using inverse operations as you do with 2-step equations.

Simplify and Solve

Example: 3x + 2 ( 2x ? 1 ) = 33

1.Use Distributive Property

3x + 4x ? 2 = 33 7x ? 2 = 33

2. Combine Like terms

3. Use Inverse Operations

+2 +2

7x = 35 7 7 x = 5

Simplify and Solve Equations

Example: 3 ( x ? 2 ) + 4x = 8

SECOND: Combine like

terms.

3x ? 6 + 4x = 8 7x ? 6 = 8

FIRST - Use the Distributive Property to

get rid of the parentheses.

Copy the rest of the problem.

Now it's a regular 2-step

equation.

+ 6 + 6 Add 6 to both sides.

7x = 14 Divide both sides by 7. 7 7

x = 2

Use your calculator for the computations if

needed.

Simplify and SOLVE:

-4y ? 5 ? 4( -2y ? 3 ) + 8 = 3

Distributive Property

- 4y ? 5 + 8y + 12 + 8 = 3

Copy the rest of

Combine like terms.

the problem. 4y + 7 + 8 = 3

4y + 15 = 3

? 15 ? 15

4y = -12 4 4 y = -3

Use your calculator for the computations if

needed.

Combine Like Terms

Simplify and Solve:

-5x + 3 ? ( 9x ? 2 ) + 7 = 96 -5x + 3 ? 9x + 2 + 7 = 96

Distributive Property

-14x + 12 = 96 ? 12 ? 12

-14x = 84 -14 -14

x = - 6

Use your calculator for the computations if

needed.

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