Basic 2-Step Equations 10/1/13A lot like 1-step equations!

Goal: Get x by itself!

Need to “undo” what is done to x.

Always do the same thing to BOTH SIDES!

Use Order of Operations backwards:

Add/Subtract first

Multiply/Divide last

Examples:

4x + 7 = 27 – 6 – 2y = 10

You Try!Solve each equation. Check your

answers!

-3x + 7 = 16 -8 = 2a + 2

5 = 7r - 2 -4 = 2 - m

Combining Like Terms 10/7/13

What are “like terms”?

Must have the same variable, or have no variable.

Terms without a variable are called “constants.”

Remember: Variables are letters!

The number before the letter is called the coefficient.

Which are like terms?

2x – 6 + 9y + 2 – 6x + 2y

To combine like terms:

Circle, underline, or box the like terms

Minus signs go with the next #

Add their coefficients!

Examples:

Simplify each expression.

4x + 2 – 2x + 1

8y – 4 + 3y

-7 + 3m – 4 – m

You Try!Simplify.

5x + 3 – 2x + 1

8x – y + 9 – 2y

a + 2a – 5 + b + 2b

You Try!

Simplify:

4m – 2n + 9 – 4m – 5

The Distributive Property 10/8/13The distributive property tells us how

to simplify expressions like: 2(x – 1)

We distribute the outside number to

both inside terms.

Like this:

Remember: “ab” means “a times b”

Examples:

Simplify.

3(2x + 1)

-2(4 – 3y)

You Try!

Simplify.

4(3x + 5)

-6(3 – 2v)

More Examples:

-(-m + 4)

(1 + 7b)6

You Try!-(-z + 5)

(4 – 3y)5

Simplifying Expressions 10/9/13

First, distribute to get rid of all

parentheses.

Then, combine like terms.

Examples:Simplify each expression.

3(4n + 2) + n

7x – (2x – 3) + 1

You Try!

Simplify each expression.

5(3x + 1) – 4x

4r – 6(1 + r)

-2(m + 5) + 6m – 1

4(x + 7) – 2(1 + 5x)

You Try! -5(2 – b) + 3b – 7

2(3k + 6) – 4(1 – 2k)

Multi-Step Equations 10/14/13

Multi-step equations have more than 2 steps.

To solve:

Simplify the side with the variables. Distribute

Combine Like Terms

Like terms may NOT cross the = sign!

Then, solve like a 1 or 2-step equation!

Examples:3(– 6 + 3x) = 18

30 = -5(6n + 6)

You Try!-6(1 – 5v) = 54

Examples:2x + 3x + 1 = 36

-26 = -7b + 6 + 3b

You Try!

8m – 3m + 7 = 17

Examples:-3(1 + 6r) + r = 14

6(6v + 6) – 5 – 6v = 1

You Try!

70 = 3(-6y – 5) – 5