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Solving Multi Step EquationsLesson 2-4 (pp. 78-83)
Lesson Objective*To simplify before solving an equation* To solve equations with variables on both sides
Reminder! Distribute if you can, then combine like terms!
WARM UP: Simplify each expression:
Today we will combine like terms and simplify in order to solve equations
1. 12d - 6 + 4d 2. 5 - 3m + 17 - 23m
3. 4(7 - 3r) 4. 9(t + 7) - 16
5. (q + 1)5 + 3q 6. 12 - 6(2r - 8)
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Notes on Solving Multi Step Equations
To simplify a side of an equation, first d____________ if you can, then combine any ________ _________.
Example 1: Solve 3n + 9 + 4n = 2
3n + 9 + 4n = 2combine like terms3n + 9 + 4n = 2
7n + 9 = 2 isolate the variable by subtracting 9 from both sides of the = sign - 9 = -9
7n = -7 isolate the variable by dividing by 7 from both sides of the = sign
7 = 7
n = -1
Check your answer: 3(-1) + 9 + 4(-1) = 2
Example 1: Simplifying before solving an equation
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Notes on Solving Multi Step Equations
Try: Solve -15 = 5b + 12 - 2b + 6
-15 = 5b + 12 - 2b + 6combine like terms
isolate the variable by subtracting 18 from both sides of the = sign
isolate the variable by dividing by 3 from both sides of the = sign
Check your answer: -15 = 5( ) + 12 - 2( ) + 6
Example 1: Simplifying before solving an equation
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Notes on Solving Multi Step Equations
To solve an equation with variables on both sides, first bring all of the v_______________ terms to one side of the e____________.
Example 2: Solve 7 + 3h = -1 - 5h
7 + 3h = -1 - 5h
isolate the variable by subtracting 7 from both sides of the = sign
isolate the variable by dividing by 8 from both sides of the = sign
Check your answer: 7 + 3(-1) = -1 - 5(-1)
Example 2: Variable on both sides
the variables need to be on the same side of the = sign. Add 5h to both sides of the = sign.
7 + 3h = -1 - 5h + 5h = + 5h
7 + 8h = -1 -7 = -7
8h = -8 8 = 8
h = -1
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Notes on Solving Multi Step Equations
Try: Solve 7b - 2 = b + 10
7b - 2 = b + 10
Check your answer: 7( ) - 2 = ( ) + 10
Example 2: Variable on both sides
isolate the variable by adding 2 on both sides of the = sign
isolate the variable by dividing by 6 from both sides of the = sign
the variables need to be on the same side of the = sign. Subtracting 1b to both sides of the = sign.
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How do you know which side to collect the variables on?
Which side has the most variables? Collect the variables on that side!!!
In the long run.... you can collect on either side : ) Take a look
1. 12y = 2y + 40 1. 12y = 2y + 40
2. 7y = y - 42 2. 7y = y - 42
3. 9 + 2p = -3 - 4p 3. 9 + 2p = -3 - 4p
-12y = -12y -2y = -2y
0 = -10y + 40 10y = + 40-40 = -40
-40 = -10y
-10 = -10
4 = y
10 = 10
y = 4
-y = -y -7y =-7y
-2p = -2p +4p = +4p
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Notes on Solving Multi Step Equations
Use the distributive property when you see a number or - sign directly next to p______________________.
Example 3: Solve 5(x - 12) = -x
5(x - 12) = -x
isolate the variable by adding 60 to both sides of the = sign
isolate the variable by dividing by 6 from both sides of the = sign
Check your answer: 5((10) - 12) = -(10)
Example 3: Using the Distributive Property
the variables need to be on the same side of the = sign. Add 1x to both sides of the = sign.
x = 10
Remember about the understood 1 : )5(x - 12) = -1x
Distribute the 55(x) - 5(12) = -1x
5x - 60 = -1x+1x = +1x
6x - 60 = 0+60 = +60
6x = 606 = 6
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Notes on Solving Multi Step Equations
Try: Solve 4a = 2(3a + 9)
4a = 2(3a + 9)
Check your answer: 4( ) = 2(3( ) + 9)
Example 3: Using the Distributive Property
isolate the variable by subtracting 18 from both sides of the = sign
isolate the variable by dividing by 2 from both sides of the = sign
the variables need to be on the same side of the = sign. Subtract 4a from both sides of the = sign.
Distribute the 2
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Practice Text page 81
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Practice Text page 81
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Practice Text page 81
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Practice Text page 81
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Practice Text page 81
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Apply
GUIDED PROBLEM SOLVING
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Apply
GUIDED PROBLEM SOLVING
Guided Problem Solving #34
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Challenge
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LESSON QUIZ 2-4
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Problem of the Day
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