4.3 Solving Two Step Equations

4.3 Solving Two Step Equations

Are you ready?

Review: One Step Equations

Multiple Choice

What is the goal of one-step equations?

• To do the opposite of everything

• To get the variable by itself

• To move all the terms to one side of the equation

Multiple Choice

How would you solve this equation:

 $15\ =\ x\ +\ 8$  

• Subtract 15 from both sides

• Add 8 to both sides

• Subtract 8 from both sides

• Add 15 to both sides

Multiple Choice

Why do we do the inverse operation to "both sides"?

• Because my teacher told me to

• To create more work

• To keep the equation balanced

Multiple Choice

What operation secretly exists in this term?

 $-3g$  

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

How would I solve:

 $-9w\ =\ 12$  

• Add 9 to both sides

• Divide both sides by -9

• Divide both sides by 9

• Multiply both sides by 12

Open Ended

Hmm....how would you solve an equation that looked like this?

 $2x+1=7$  

Welcome to Two Step Equations

Goal: ISOLATE THAT VARIABLE

Multiple Choice

What is our goal for two step equations?

• Isolate the variable

• Combine like terms

• Get an answer

How to Solve ANY Two-Step Equation

• 1. What operation do you see?

• 2. How can you "undo" it?

• 3. Repeat until variable has been isolated

Multiple Select

Let's go back to our first equation:

 $2x+1=7$  

What operations do you see in this equation? Select ALL that apply.

• Addition

• Subtraction

• Multiplication

• Division

2x + 1 = 7

This equation has ADDITION + MULTIPLICATION in it.

We must undo each of these operations to get X by itself.

Which one do we start with?

ADDITION!

You always want to UNDO any ADDITION or SUBTRACTION FIRST

Multiple Select

You got that? What operations should we always undo FIRST?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

So what would the first step be when solving:

 $2x+1=7$  

• Subtract 2x from both sides

• Subtract 7 from both sides

• Subtract 1 from both sides

• Divide both sides by 2

Let's do it

 $2x+1=7$  
           -1      -1   
        2x = 6

Multiple Choice

Now what? We have

 $2x=6$  left over.

• Divide both sides by 2

• Multiply both sides by 2

Last step!

 $\frac{2x}{2}=\frac{6}{2}$  

 $x=3$  

Think of 2-Step Equations like a bad Love Triangle

First, get rid of the "third wheel". And then separate the couple.

Let's try to solve:

6x + 8 = 50

Fill this in on your note sheet!

Let's try to solve:

2x - 5 = 11

Fill this in on your note sheet!

Hmm what about...

 $7-3x=34$  

Fill this in on your note sheet!

Hmm what about...

 $\frac{x}{2}-7=9$  

Fill this in on your note sheet!

Poll

How do you feel about solving two-step equations?

• 1 - Not doing well AT ALL

• 2 - Mind blown, but I can do this.

• 3 - Ehh, I need to practice

• 4 - It makes sense! I can do this on my own.

• 5 - Easy! I could help others solve these equations!