Two Step Equations

Solving Multi-Step Equations

Overview

Today's Learning Objective:

"I can solve multi-step equations."

In this presentation, you will learn:

●How to solve multi-step equations
●How to combine like terms before solving
●How to use the Distributive Property to simplify

Review: Using Inverse Operations

Solve using inverse operations.

y - 17 = 24

3x + 9 = 45

Review: Using Inverse Operations

Solve using inverse operations.

y - 17 = 24

+17 +17

y = 41

3x + 9 = 45

-9 -9
3x = 36
/3 /3
x = 12

Multiple Choice

What is the first step in solving the following equation:

$$-3x+17=-1$$

• Add 3 to both sides

• Subtract 17 from both sides

• Add -3 and 17

• Divide both sides by -3

Drag and Drop

Solve this equation $$-3x+17=-1$$

​

Placeholder

Drag these tiles and drop them in the correct blank above

6

-6

-13

13

Review: Simplifying Expressions

Combining Like Terms

12d + 6 - 4d

Using the Distributive Property

4(3x - 6)

Review: Simplifying Expressions

Combining Like Terms

12d + 6 - 4d

8d + 6

Using the Distributive Property

4(3x - 6)

12x - 24

Solving Mult-Step Equations

You have solved equations and simplified algebraic
expressions. Now you will need both of these skills to solve
new types of equations. Often, you need to simplify at least
one side of an equation before solving it.

To simplify an equation, combine any like terms and use the
Distributive Property with expressions as needed.

Match

Match the following

• 2x+3-x

• 4d-x+5x

• 4d+2d-5x-x

• -2(2d+x)

• 3x+2x+3

x+3

4d+4x

6d-6x

-4d-2x

5x+3

• x+3

• 4d+4x

• 6d-6x

• -4d-2x

• 5x+3

Math Response

Simplify the expressions below:

$$-x+\left(\frac{1}{3}x+9-2\right)$$

Type answer here

Correct Answer: -\frac{2}{3}x+7

Deg^°

Rad

As always, you solve to find the value of the variable.

Combining Like Terms

Solve 3n + 9 + 4n = 2.

3n + 9 + 4n = 2
7n + 9 = 2

-9 -9
7n = -7
/7 /7
n = -1

Combining Like Terms

Check 3n + 9 + 4n = 2.

3(-1) + 9 + 4(-1) =? 2
-3 + 9 + -4 =? 2
6 + -4 =? 2

2 = 2

Make sure to check
your solution in the
ORIGINAL equation.
Just in case you made

a mistake when

simplifying!

You Try It!

Work with your group to solve the following equation. Take
turns writing each step. Don't forget the check step!

5x + 12 - 2x = -15

3x + 12 = -15
-12 -12
3x = -27
/3 /3

x = -9

Using the Distributive Property

Solve 2(x - 1) = 16.

2(x - 1) = 16
2x - 2 = 16
+2 +2
2x = 18
/2 /2
x = 9

Math Response

Solve:

$$\frac{1}{4}b+2=18$$

b=_______

Type answer here

Correct Answer: 64

Deg^°

Rad

Math Response

Solve:

$$5x+27=122$$

x=_______

Type answer here

Correct Answer: 19

Deg^°

Rad

Using the Distributive Property

Check 2(x - 1) = 16 for x = 9.

2(9 - 1) =? 16
2(8) =? 16
16 = 16

Steps for Solving Equations

Just like we have an order of operations - PEMDAS - we have
a specific order we must follow for solving equations!

STEP 1 - Use the Distributive Property to clear parentheses

STEP 2 - Combine like terms

STEP 3 - Use inverse operations to isolate the variable

Math Response

Solve the following equation:

$$-\left(3x+21\right)+x=21$$

Type answer here

Correct Answer: -21

Deg^°

Rad

Multiple Select

Which equations are equivalent to

$$\frac{1}{2}\left(4+8x\right)=17$$

• 2+4x=17

• 4x=15

• 2+4x=8.5

• 4+8x=34

Reorder

Put the steps to solve the following equation in order.

$$-4\left(1.75+x\right)=18$$

• $$-7-4x=18$$

• $$-4x=25$$

• $$x=-6.25$$

1

2

3

• 1
• 2
• 3