Do these FAST!

• Solve for x.

1. x – 7 = 19

2. 21 – x = 36

3. 9x = 45

4. 6x = 15

5. x/15 = 3

Answers:

1. x = 262. x = -153. x = 5

4. x = 5/25. x = 45

Multi-Step Equations

Coordinate

Algebra

Essential Question

• How do I solve multi-step equations?

Multi-Step Equations

• Equations that contain 2 or more different operations in order to solve the problem.

• There will also be equations with variables on both sides.

Solve:

A.) 4x – 7 = 9

B.) -9x + 3 = 30

A.) x = 4

B.) x = -3

Solve:

C.)

D.)

C.) x = 20

D.) x = -80

625

x

2610

x

Solve:

E.)

F.)

53

4

d

29

5

c

E.) x = 19

F.) x = -13

Tough one!

2

54

3

2x

x = 4

9

Multi-step equations

• Multi-step equations contain more than one of the same variable. Sometimes these variables are on opposite sides of the equal symbol.

• ISOLATE your variable on one side of the equation.

5x – 7 = x + 3

Example 1

• 5x – 7 = x + 3

-x -x____

4x – 7 = 3

+7 +7

4x = 10

4 4

x = 5

2

• Step A:

Use Addition/Subtraction Properties of Equality to separate all variable terms from number terms on opposite sides of the equal symbol.

• Step B:

Solve for x. ALWAYS reduce fractions!

• Step C:

Check Solution.

Variable terms already together

• DO NOT use addition or subtraction property of equality. Simply combine like terms as they are, where they are!

2x + 3x = 255x = 25

x = 5

If you see Parentheses . . .

• Then your 1st step will be to use the DISTRIBUTIVE PROPERTY

• After ( )’s are gone, then follow steps A-C from example 1.

Example 2

• 2(2x + 3) = -4x + 64x + 6 = -4x + 6

+4x +4x___ 8x + 6 = 6

- 6 - 6 8x = 0

8 8x = 0 (not 8 or undefined)

Example 3

• -(3x + 5) = 5x + 1-3x - 5 = 5x + 1

+3x +3x___ -5 = 8x + 1

-1 - 1 -6 = 8x

8 8x = -3/4

Summarizer

• What operation(s) do you start with when solving a multi-step equation?

• Addition OR Subtraction!

HOMEWORK

• worksheet