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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Bell Ringer
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.
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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