Solving equations with multiplication and division

Your friend’s mountain bike cost $245 more than his skateboard. His mountain bike cost $290. How much did your friend’s skateboard cost?

Write an equation and solve

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Adding and Subtracting Integers

Properties of addition

Multiplying and Dividing Integers

Solving one-step equations with addition and subtracting

Where were…

Discuss…◦ What is the goal when solving equations?

◦ What are the steps to solve this problem?

◦ What allows me to do those steps? Properties? Concepts?

x – 21 = 5

Students will learn to…

◦ Solve one-step equations with multiplication and division.

Where we are…

Integer Operations Assessment◦ Thursday◦ Friday

Where we are going…

Key Vocabulary for Solving Equations Inverse operation

Isolate the variable

Multiplication Property of Equality◦ If you multiply each side of an equation by

the same number, the two sides remain equal.

Division Property of Equality◦ If you divide each side of an equation by the

same nonzero number, the two sides remain equal.

Solving Equations Algebraically 4x = 32 Goal: Isolate the

variable

Question: How can I get the variable by

itself?

Think… What is the inverse operation of multiplicationorThink… What is the opposite of multiplying by 4?

Solving Equations Algebraically 4x = 32 4 4 x = 8

Goal: Isolate the variable

Question: How can I get the variable by

itself?

Think… What is the inverse operation of multiplicationorThink… What is the opposite of multiplying by 4?

Solving Equations Algebraically 10x = 150

How did you get your answer?

Describe what you were thinking...

What was difficult about that concept?

Solving Equations Algebraically 10x = 150 10 10 x = 15

How did you get your answer?

Describe what you were thinking...

What was difficult about that concept?

Solving Equations Algebraically = 10

Goal: Isolate the variable

Question: How can get the variable by

itself?

How did you get your answer?

Describe what you were thinking...

What was difficult about that concept?

Solving Equations Algebraically 5 x = 10 x 5 c = 50

Goal: Isolate the variable

Question: How can get the variable by

itself?

How did you get your answer?

Describe what you were thinking...

What was difficult about that concept?

Solving Equations Algebraically = 12 Goal: Isolate the

variableMultiply both sides

by 3

How did you get your answer?

Describe what you were thinking...

What was difficult about that concept?

Can you solve one-step equations w/ multiplication and division????

pg. 356 #3-6, 24, 26

Homework

Solve one-step equations w/

multiplication and division.

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A number multiplied by three is 27.

A number divided by eight is two.

A number tripled and increased by ten is 22.

Bell Ringer

Adding and subtracting Integers Multiplying and dividing Integers Properties of Addition Properties of Multiplication Solving one-step equations

Where we were…

Homework…

Students will learn to…

◦ Solve 2-step equations.

Where we are…

Discuss…◦ What operations are involved in this problem?◦ How many terms?◦ In order of operations, what do we do first?

3x + 10=22

Solve 2 step equations.

Goal: Isolate the variable

Question: How can I get the variable by

itself?

Without guess and check, what steps are used to solvethis equation?

How is this process related to the order of operations?

x = 4

3x + 10 = 22

Order of Operations – backwards◦ 1) Combine like terms◦ 2) Undo addition or subtraction◦ 3) Undo multiplication or division

Like terms: 3x + 5 + 5 = 22

Solving 2 step equations.

Simplify by combining like terms◦ 5x + 12 + (-9) = 8◦ 5x + 3 = 8

Undo addition or subtraction◦ 5x + 3 = 8◦ - 3 = -3◦ 5x = 5

Undo multiplication or division◦ 5x = 5◦ 5 5◦ x = 1

5x +12 - 9 = 8

Simplify by combining like terms◦ 2x + x + 10 = 25◦ 3x + 10 = 25

Undo addition or subtraction◦ 3x + 10 = 25◦ - 10 = -10◦ 3x = 15

Undo multiplication or division◦ 3x = 15◦ 3 3◦ x = 5

2x + x + 10 = 25

Simplify by combining like terms Undo addition or subtraction

◦ - 5 = 20◦ + 5 = +5◦ = 25

Undo multiplication or division◦ = 25◦ 2• = 25•2◦ x = 50

- 5 = 20

Can you hit the learning target?

- 15 = 100

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solving the problem.◦ Submit

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