section 1-5
DESCRIPTION
Solving EquationsTRANSCRIPT
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Section 1-5Solving Equations
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Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
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Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
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Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
![Page 5: Section 1-5](https://reader034.vdocument.in/reader034/viewer/2022052621/5584901dd8b42a05388b466d/html5/thumbnails/5.jpg)
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
![Page 6: Section 1-5](https://reader034.vdocument.in/reader034/viewer/2022052621/5584901dd8b42a05388b466d/html5/thumbnails/6.jpg)
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
![Page 7: Section 1-5](https://reader034.vdocument.in/reader034/viewer/2022052621/5584901dd8b42a05388b466d/html5/thumbnails/7.jpg)
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
6i75 = 16
xi6
![Page 8: Section 1-5](https://reader034.vdocument.in/reader034/viewer/2022052621/5584901dd8b42a05388b466d/html5/thumbnails/8.jpg)
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
6i75 = 16
xi6
x = 450
![Page 9: Section 1-5](https://reader034.vdocument.in/reader034/viewer/2022052621/5584901dd8b42a05388b466d/html5/thumbnails/9.jpg)
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
6i75 = 16
xi6
x = 450
Matt won $450.
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What did we do to solve this problem?
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What did we do to solve this problem?
Read the problem
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What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
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What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
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What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
Set up the problem
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What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
Set up the problem
Solve
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What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
Set up the problem
Solve
Answer the question
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Example 13x + 7 = 25
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Example 13x + 7 = 25
-7
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Example 13x + 7 = 25
-7 -7
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Example 13x + 7 = 25
-7 -7
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Example 13x + 7 = 25
-7 -7
3x
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Example 13x + 7 = 25
-7 -7
3x =
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Example 13x + 7 = 25
-7 -7
3x = 18
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Example 13x + 7 = 25
-7 -7
3x = 183 3
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Example 13x + 7 = 25
-7 -7
3x = 183 3
x = 6
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Distributive Property:
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Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
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Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Opposite of a Sum Theorem:
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Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Opposite of a Sum Theorem:
For real numbers a, and b:
-(a + b) = -a + -b
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Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Opposite of a Sum Theorem:
For real numbers a, and b:
-(a + b) = -a + -b
Note: The “-” here stands for “opposite”
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Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
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Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
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Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
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Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
46 = 7x − 3
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Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
46 = 7x − 3
49 = 7x
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Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
46 = 7x − 3
49 = 7x
x = 7
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Clearing out fractions
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Clearing out fractions
Face it, most of you hate them, so how do you get rid of them?
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Clearing out fractions
Face it, most of you hate them, so how do you get rid of them?
Multiply both sides of the equation by a common denominator
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Example 3
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Example 3
16
a + 25
a +10 = 346
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Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
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Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
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Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
17a + 300 = 10380
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Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
17a + 300 = 10380
17a = 10080
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Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
17a + 300 = 10380
17a = 10080
a =
10080
17
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Example 4
.04b + .08(b − 3) = 12
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Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
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Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
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Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
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Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
12b − 24 = 1200
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Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
12b − 24 = 1200
12b = 1224
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Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
12b − 24 = 1200
12b = 1224
b = 102
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Homework
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Homework
p. 33 #1 - 27