3.3 Solving Multi-Step Equations

• To use two or more steps to solve equations.

Solving a Linear Equation

• Sometimes solving a Linear Equation can require using more then one step to undo operations

• When solving Multi-Step Linear equations, make sure you Simplify each side of the equation (each expression) if needed before undoing any operations.

Ex 1: Multi Step w/Multiplication

CHECK!

3x + 7 = -8

3(-5) + 7 = - 8

-15 + 7 = -8

-8 = -8

True!

-5 is a solution to this equation!

Now You Try…

1. 6x – 15 = 9

2. –4 + 7x = –11

3. 1 = 5 + 2y

4. –3x + 1 = –8 -2 = yx = 4

x = -1 x = 3

Ex 2: Multi Step w/Division

Ex 2B: Multi Step w/Division

Since the entire left side is being divided by 9, I have to undo that operation first!

Compare…

You Try!

1. 2.

3. 4.

Ex 3: Multi Step w/Fraction

Ex 4: Simplify First!

Combine Like Terms!

Check 7x – 3x – 8 = 24!

7x – 3x – 8 = 24

7(8) – 3(8) – 8 = 24

56 – 24 – 8 = 24

24 = 24

TRUE

8 is a Solution!

You Try…

1. 3r – r + 15 = 41

2. -8 + 5a – 2 = 20

3. 13 = 12t – 5 – 3t

r = 13

a = 6

2 = t

Use the Distributive Property

8 x – 2(x + 7) = 16

8 x – 2(x + 7) = 16

8 x – 2x – 14 = 16

8 x – 2x – 14 = 16

6x – 14 = 16

6x = 30

x =5

Distribute

Combine Like Terms Undo – 14

Undo 6 times

Let’s do another…

5x + 3 (x + 4) = 28

5x + 3 (x + 4) = 28

5x + 3x + 12 = 28

8x + 12 = 28

8x + 12 – 12 = 28 – 12

8x = 16

x =

X = 2

You Try…

1. 6(x + 2) = 15

2. 8 – 4(x + 1) = 8

3. 3m + 2(m - 5) = 10

x = 1/2

x = -1

m = 3