Three Step Equations Lesson

Multi-step Equations

By:Jeremiah Neal

Learning Objective:

I can understand strategies for solving for multi-step equations.

I can learn how to use multi-step equations to solve real-world problems.

Multi-step Equations

5(y-2)-7y = -32

Example:

• Distribute (if needed)

• Combine Like Terms (if needed)

• Identify the Variable

• Inverse Operation on the Constant

• Inverse Operation on the Coefficient

• Check Yourself

Steps:

Distributive Property

3(4x -7) =15

Example:

• Distribute

• Identify the Variable

• Inverse Operation on the Constant

• Inverse Operation on the Coefficient

• Check Yourself

Steps:

Combining Like Terms

3b + 4 - 5b + 7b - 8 = 21

Example:

• Combine Like Terms

  (Circle, Circle, Square, Square)

• Identify the Variable

• Inverse Operation on the Constant

• Inverse Operation on the Coefficient

• Check Yourself

Steps:

• Inverse means opposite

• When we solve equations using inverse operations we will be using the opposite operation for the symbol we see

• Addition and Subtraction are opposites

• Multiplication and Division are opposites

​Example 1

​2x + 12 = 6x - 4

​Step 1 : Subtract 2x from each side. 2x - 2x + 12 = 6x - 2x - 4 ; 12 = 4x - 4

​Step 2 : Add 4 to each side. 12 + 4 = 4x - 4 + 4 ; 16 = 4x

​Step 3 : Divide 4 from each side. 16/4 = 4x/4 ; 4 = x

​

​Answer : x = 4

Multiple Choice

What do you think a Multi-step equation is?

• An algebraic expression that requires more than one operation, such as subtraction, addition, multiplication,or division to solve

• An rate for one of something

• P.E.M.D.A.S

• An relationship between two variables where their ratios are equivalent

Multiple Choice

$$96=6\left(k+8\right)$$  

• $$12$$  

• $$8$$  

• $$-4$$  

• $$9$$  

Multiple Choice

Solve for v.

• 60
• -3
• 15
• 3

Multiple Choice

In a basketball tournament, Team A scored 5 fewer than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Write an equation to represent this scenario using the variable b to represent Team B’s total points. Which equation represents this situation?

• 2(b - 5) + b + (b + 80) = 983

• (2b - 5) + (b + 80) + 983 = b

• (2b - 5) = (b + 80) + b

• (2b - 5) + b + (b + 80) = 983

Multiple Choice

In a basketball tournament, Team A scored 5 fewer than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Write an equation to represent this scenario using the variable b to represent Team B’s total points. What expression represent the points for Team C?

• b

• b + 80

• 2(b - 5)

• 2b - 5

Fill in the Blanks

5 (y - 2) - 7y = -32

What is the first step?

Fill in the Blanks

5y - 10 - 7y = -32

What is the step is after distributing?

Fill in the Blanks

Solve: -10 - 2y = -32

Fill in the Blanks

Word Problem Practice: The class of 27 students is taking a trip to an amusement park! The back of your notes tells you if you have a regular ticket or a regular ticket with a FastPass ($25) add-on. The total cost of the trip for the class was $1600.

Write a multi-step equation to help solve how much each ticket cost.

 

Fill in the Blanks

Using your equation from the previous question, how much does one ticket cost?