**Solving Two-Step Equations**

Let's Review One-Step Equations:

Ogres and Two-Step Equations

Two-Step Equation

HINT: Start from the

OUTSIDE

layer

Example: 5

X

- 6 = 9

Layer 1:

Add 6 to both sides

Layer 2:

Divide both sides by 5

**Warm-Up!**

Y - 5 = 2

Finish the phrase:

Ogres are like onions, and two-step equations, they all have . . .

**LAYERS!**

**5X + 3 = 8**

Example 1 :

Example 2 :

5X - 6 = 9

+6 +6

5X = 15

5 5

X = 3

-3 + 2W = 11

-10 = 6 + 4X

Work this problem and bring it to class:

Name:

4Y - 9 = 15

**Two-Step Equations**

**Definition:**

An equation that needs

two steps

to solve

An equation that needs

two steps

to solve

Outside Layer?

5X - 6 = 9

How do you get to the center of an onion?

How do you isolate the variable?

WARM-UP ANSWER

Y - 5 = 2

+5 +5

Y = 7

More Review of One-Step Equations:

Y = 2

5

3x = 12

A.

B.

Answers

y = 2

5

y = 5 (2) = 10

3x = 12

A.

B.

3x = 12 = 4

3

3

y = 2

5

(5)

(5)

-3 + 2W = 11

Answer

The outside layer is the -3.

+3

Do the opposite to both sides.

+3

2W = 14

What operation is 2 doing to W? (add, subtract, multiply, or divide)

Do the opposite to both sides.

2

2

W = 7

Simplify

-10 = 6 + 4X

The outside layer is the 6. (work on the side the variable is on.)

Do the opposite to both sides.

-6

-6

-16 = 4x

What operation is 4 doing to X? (add, subtract, multiply, or divide)

Do the opposite to both sides.

4

4

Simplify.

-4 = X

http://bcontext.com//bfile/player/dlqdr/?auth=N3PJ3MTJLXZZF5JEJCLM9S8HK3RAU10BLNPOKNLP3YZUOR8YHX

Please watch this.

Another Way of Looking At It

In the morning you put on socks first, then your shoes.

When you undress, you take off your shoes then your socks.

Opposite order, opposite action.

Put On - Socks

Put On - Shoes

Take Off - Shoes

Take Off - Socks

1.

1.

2.

2.

Order of Operations is like the Shoes and Socks

2x + 3 = 15

Step 1

How do we make "x" look like "2x + 3" using order of operations?

First we multiply by 2. (x becomes 2x)

Then we add 3. (2x becomes 2x + 3)

Step 2

Solve the problem by working "backwards"

Subtract 3

Divide by 2

2x + 3 = 15

- 3 -3

2x = 12

2 2

x = 6

G G

E E

M M

D D

A A

S S

do

undo

Opposite order

Opposite operation

Do

Undo

2h + 9 = 21

-9 -9

2h = 12

2h = 12

2 2

h = 6

Step 1: 9 was added to 2h so we subtract 9 from BOTH sides

Step 2: h was multiplied by 2 so we divide BOTH sides by 2

We are trying to find x.

What happened to x? It was multiplied by 5. Then 6 was subtracted. 6 is the outside layer

5 is an inside layer because it was last.