Solving Two-Step Equations

What is a Two-Step Equation?

An equation written in the form

Ax + B = C

a) 3x – 5 = 16

b) y/4 + 3 = 12

c) 5n + 4 = 6

d) n/2 – 6 = 4

Examples of Two-Step Equations

1. Solve for any Addition or Subtraction on

the variable side of equation by “undoing”

the operation from both sides of the

equation.

2. Solve any Multiplication or Division from

variable side of equation by “undoing” the

operation from both sides of the equation.

Steps for Solving Two-Step Equations

PEMDAS in Reverse…

Addition Subtraction

Opposite Operations

Multiplication Division

Identify what operations are on the variable

side. (Add, Sub, Mult, Div)

“Undo” each operation by using the

opposite operation.

Whatever you do to one side, you must do

to the other side to keep the equation

balanced.

Helpful Hints?

4x – 5 = 11

+5 = +5 (Add 5 to both sides)

4x = 16 (Simplify)

4 = 4 (Divide both sides by 4)

x = 4 (Simplify)

Ex. 1: Solve 4x – 5 = 11

2x – 5 = 17

3y + 7 = 25

Try These Examples

5n – 2 = 38

12b + 4 = 28

x = 11

y = 6

Check your answers!!!

n = 8

b = 2

x 3 + 4 = 9

- 4 = - 4 (Subtract 4 from both sides)

x 3 = 5 (Simplify)

(x 3) 3 = 5 3 (Multiply by 3 on both sides)

x = 15 (Simplify)

Ex. 2: Solve x 3 + 4 = 9

x 5 – 3 = 8

c 7 + 4 = 9

Try these examples!

r 3 – 6 = 2

d 9 + 4 = 5

x = 55

c = 35

Check your answers!!!

r = 24

d = 9

1. Make sure your equation is in the form

Ax + B = C

2. Keep the equation balanced.

3. Use opposite operations to “undo”

Follow the rules (PEMDAS in Reverse):

1. Undo Addition or Subtraction

2. Undo Multiplication or Division

Time to Review!

Wait! There’s more…

Solving Multi-Step Equations

What is a Multi-Step Equation?A multi-step equations takes more than two steps to solve.

The same rules for two-step equations apply, but now you have equations that require you to do additional work BEFORE you begin to isolate the variable.

a) 8x - 3x - 10 = 20

b) 7x + 2(x + 6) = 39

c) (3x + 5) = -24

Examples of Multi-Step Equations

3

2

1. Start by simplifying one or both sides of the

equation. This may require:

a. Combining like terms

b. Using the distributive property

c. Multiplying by a reciprocal

2. Use inverse operations (PEMDAS in

reverse) to isolate the variable.

Steps for Solving Multi-Step Equations

8x – 3x – 10 = 20 Original equation

5x – 10 = 20 Combine like terms

+10 = +10 Add 10 to both sides

5x = 30 Simplify

5 = 5 Divide both sides by 5

x = 6 Simplify

Ex 1: 8x - 3x - 10 = 20

7x + 2(x + 6) = 39 Original equation

7x + 2x + 12 = 39 Distributive property

9x + 12 = 39 Combine like terms

-12 = -12 Subtract 12 from both sides

9x = 27 Simplify

9 = 9 Divide both sides by 9

x = 3 Simplify

Ex 2: 7x + 2(x + 6) = 39

(3/2)(3x + 5) = -24 Original equation

·(2/3) = ·(2/3) Multiply by reciprocal

3x + 5 = -16 Simplify (-24/1 * 2/3 = -48/3 = -16)

-5 = -5 Subtract 5 from both sides

3x = -21 Simplify

3 = 3 Divide both sides by 3

x = -7 Simplify

Ex 3: (3x + 5) = -24 3

2

12v + 14 + 10v = 80

3 + 4(z + 5) = 31

Try these examples!

5h + 2(11 – h) = -5

(3/2)(x – 5) = -6

v = 3

z = 2

Check your answers!!!

h = -9

x = 1

TB pp. 144-145 #1, 3, 7, 11, 15, 19, 21, 22, 25, 27, 31, 35, 40

TB pp. 150-151 #1, 5, 11, 13, 17, 18, 19, 23, 27, 31

Homework