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 Examples5n – 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 Subtraction2. 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

32

1. Start by simplifying one or both sides of the equation. This may require:a. Combining like termsb. Using the distributive propertyc. 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 equation7x + 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 32

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