Rules to Remember

• When solving an equation, the goal is to get the variable by itself.

• Addition and Subtraction are inverse operations. (opposites)

• Multiplication and Division are inverse operations. (opposites)

Don’t Forget

• The equation is like a balance scale. Whatever you do to one side of the equation must be done to the other side of the equation.

How to solve two-step equations

• “Undo” the operations in the reverse order of the order of operations.

• You are using the work back-words strategy

• In order of operations we do multiplication or division first, then addition and subtraction. When solving an equation we do the opposite!

Integer Rules to Remember• Adding Integers1. Same sign= add and keep the sign2. Different sign = subtract and keep the sign of the larger

number• Subtracting Integers1. Keep, Change, Change2. Follow the rules for addition• Multiplying and Dividing Integers1. Same Sign = Positive Answer 2. Different Sign = Negative Answer

Let’s Try One…

• 3x + 2 = 23 - 2 -2 21

3x = 21 3 3 x = 7

The problem contains addition and multiplication. Which one do we undo 1st?

Another Example

• -2y – 7 = 3 +7 +7 10 -2y = 10 -2 -2 y = -5

The problem contains subtraction and multiplication. Which one do we undo 1st?

Last Example

• -3c + 9 = 3 -9 -9 -6 -3c = -6 -3 -3 c = 2

The problem contains addition and multiplication. Which one do we undo 1st?

5) Solve 3 27a

-3 -3

a = 35

1. Draw “the river”2. Subtract 3 from both

sides3. Simplify4. Clear the fraction –

Multiply both sides by -7

5. Simplify6. Check your answer

D U

÷ -7+ 3

- 3· -7

Do/Undo Chart – This one is tricky! Remember to always use the sign in front of the number.

57a

7 5 77a

3 2357

3 5 2

3) Solve d 4

23

d – 4 = 6 + 4 + 4 d = 10

1. Draw “the river”2. Clear the fraction -

Multiply both sides by 2

3. Simplify4. Add 4 to both sides5. Simplify6. Check your answer

D U

- 4÷ 2

· 2+ 4

42 3 22d

10 4 32

- 1 - 1

5 · · 5 3x = 15 3 3 x = 5

7) Solve 3 1 45x

1. Draw “the river”2. Subtract 1 from both

sides3. Simplify4. Clear the fraction -

Multiply both sides by 5

5. Simplify6. Divide both sides by 37. Simplify8. Check your answer

D U

· 3 ÷ 5+ 1

- 1· 5÷ 3

3 35x

3( ) 1 455

REVIEW: Simplify Using the Distributive Property.

Distributive Property – Multiply times everything in the parentheses.

a ( b + c ) = ab + ac

Example 1: -3 ( x + 5 )

-3x – 15

Example 2: -7 ( 2a – 4 )

-14a + 28

OR a ( b – c ) = ab – ac

REVIEW: Simplify Using Combining Like Terms

Like Terms must have the same variables and the same powers on the letters. Combine like terms by adding or subtracting the coefficients (numbers in front of the variables).

Example 1: 3x + 5 – 7x + 9

-4x + 14Example 2: 3 – 6y – 7 – 9y

-4 – 15y

How do we simplify and solve How do we simplify and solve equations with multiple steps?equations with multiple steps?

To solve equations with multiple steps, first use the distributive property to get

rid of the parentheses.

Then, combine like terms to get the problem in the 2-step form.

Solve by using inverse operations as you do with 2-step equations.

Simplify and Solve

Example: 3x + 2 ( 2x – 1 ) = 33

4x – 2 3x + = 33

7x – 2 = 33+ 2 + 2

7x = 357 7x = 5

1.Use Distributive Property

2. Combine Like terms

3. Use Inverse Operations

Simplify and Solve EquationsExample: 3 ( x – 2 ) + 4x = 8

FIRST - Use the Distributive Property to

get rid of the parentheses.3x – 6 + 4x = 8

Copy the rest of the problem.

SECOND: Combine like

terms.7x – 6 = 8

+ 6 + 67x = 14 Divide both sides by 7.7 7

x = 2

Add 6 to both sides.Now it’s a regular 2-step

equation.

Use your calculator for the computations if

needed.