Solving Multi-Step Equation (On one side)

Solving Multi-Step Equation (On one side)

by Cynthia Huang

Solving Multi-Step Equations

Lesson Goal- To solve equations that involve multiple steps using inverse operations

Solving Multi-Step Equation Steps:

Step 1) Distributive Property

Step 2) Combine like terms (on the same side of the equation)

​Step 3) Isolate the variable and Solve.

Multiple Choice

What is the first thing you should do to simplify an equation?

• add

• Distributive Property

• Combine like terms

• divide

Multiple Choice

What is the first step in solving the equation 2a - 4(a - 5) = 10

• Add 4 to both sides
• Add the 2a and a 
• Distribute 4 across the ( ).

• Distribute -4 across the ( ).

Multiple Select

Which of the following equations require you to use the Distributive Property first?

Select all that apply.

• 6x-8=7(x+2)

• 7n-5=3

• 2(a-9)=9a+1

• 4-9y=8+4y-2

Multiple Choice

Let's Practice using the Distributive Property.

6 (x-3)

• x-18

• 6x+18

• 6x-18

• 6x-9

Multiple Choice

Practice using the Distributive Property:

-3(n-8)

• 3n-8

• -3n-24

• -3n+24

Multiple Choice

Solve:

3(3x - 6) = 18

• x = 4

• x = -4

• no solution

• infinite solutions

Once you distribute, check to see if you have like terms, on the same side of the equal sign. Here are some examples of like terms:

• 5x and -6x

• -6 and 3 ***Remember that constants (regular numbers) are like terms with each other.***

• 7m and m

Multiple Select

Check the boxes that show like terms. (Select ALL that apply.)

• 5 and -8

• 4n and -8x

• -9 and 9x

• 1 and 7

• 6y and 8y

Multiple Choice

Let's practice combining like terms.

7x - 8 + 3x - 1

• 10x-9

• 21x+8

• 4x+9

• 10x+9

Multiple Choice

What Step is first in this problem?

3a + 9 + 4a = 2

• Combine Like Terms

• Distributive Property

• +9 to both sides

• -9 to both sides

Multiple Choice

What is the equation after you have Combined Like Term?

3a + 9 + 4a = 2

• 7a + 9 = 2

• 12a + 4 = 2

• 13a + 9 = 2

• 16a = 2

Multiple Choice

Now that you have Combine Like Terms. Solve for a.

3a + 9 + 4a = 2

7a + 9 =2

• a = 1

• a = -1

• a = 11/7

• a = -11/7

Multiple Choice

What Step is first?

-15 = 5a +12- 2a + 6

• Combine Like Terms

• Distributive Property

• +6

• +12

Multiple Choice

Once you have Combine Like Terms. What is the equation now?

-15 = 5a + 12 - 2a + 6

• -15 = 3a + 18

• -15 = 7a + 18

• -15 = 15a + 6

• -15 = 21a

Multiple Choice

You Combined Like Terms. Now solve for a.

-15 = 5a + 12 - 2a + 6

-15 = 3a + 18

• 11 = a

• -11 = a

• 1 = a

• -1 = a

Poll

How did you feel when solving the questions on the last 2 slides?

Distribute, then combine any like terms on the same side!

This video will help with slides 11 and 12. Notice how they are distributing a negative!!!

Multiple Choice

3x + 2(4x - 4) = 3

• 4

• 3

• 2

• 1

Multiple Choice

6x + 3(-x + 11) = 3

• -10
• 10
• 15
• -15

Poll

How did slides 12 and 13 go?

• I got this!

• It is starting to get a little easier.

• I am starting to get a little bit confused.

• You've lost me...send help!