Variables%20and%20Expressions

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Variables and Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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Warm Up Evaluate. 1. 21 ? 2(3)
15
31
2. 4 3 ? 9
21
3. 2(9) (3)
4. 6(1.4) 12
20.4
15.3
5. 7(2.9) ? 5
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Problem of the Day Miss Smith obtained the
prices below from the landscape company. She
plans to buy five birch, two elm, one dogwood,
and two oak trees. The landscape company will
charge her 15 to plant each tree. How much will
it cost?
337.90
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Learn to evaluate algebraic expressions.
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Vocabulary
variable coefficient algebraic expression constant
evaluate substitute
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A variable is a letter that represents a value
that can change or vary.
The coefficient is the number multiplied by the
variable.
Coefficient
Variable
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An algebraic expression has one or more variables.
In the algebraic expression x 6, 6 is a
constant because it does not change.
To evaluate an algebraic expression, substitute a
given number for the variable, and find the value
of the resulting numerical expression.
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Additional Examples 1A Evaluating Algebraic
Expressions with One Variable
Evaluate each expression for the given value of
the variable.
x 5 for x 12
Substitute 12 for x.
12 5
Subtract.
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Additional Examples 1B Evaluating Algebraic
Expressions with One Variable
Evaluate each expression for the given value of
the variable.
2y 1 for y 4
Substitute 4 for y.
2(4) 1
Multiply.
8 1
Add.
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Additional Example 1C Evaluating Algebraic
Expressions with One Variable
Evaluate the expression for the given values of
the variable.
6(n 2) 4 for n 5, 6, 7
6(5 2) 4
6(7) 4
42 4
38
6(6 2) 4
6(8) 4
48 4
44
6(7 2) 4
6(9) 4
54 4
50
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Check It Out Examples 1
Evaluate each expression for the given value of
the variable.
A. x 5 for x 3
Substitute 3 for x.
3 5
Add.
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B. 4c 1 for c 11
Substitute 11 for c.
4(11) 1
Multiply.
44 1
Add.
45
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Check It Out Example 1
Evaluate the expression for the given values of
the variable.
C. 5(n 3) 2 for n 3, 4, 5
5(3 3) 2
5(6) 2
30 2
28
5(4 3) 2
5(7) 2
35 2
33
5(5 3) 2
5(8) 2
40 2
38
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Additional Example 2 Evaluating Algebraic
Expressions with Two Variables
Evaluate each expression for the given values of
the variables.
A. 4x 3y for x 2 and y 1
4(2) 3(1)
Substitute 2 for x and 1 for y.
Multiply.
8 3
Add.
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B. 9r 2p for r 3 and p 5
Substitute 3 for r and 5 for p.
9(3) 2(5)
Multiply.
27 10
Subtract.
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Check It Out Example 2
Evaluate each expression for the given values of
the variables.
A. 3x 2y for x 3 and y 4
3(3) 2(4)
Substitute 3 for x and 4 for y.
Multiply.
9 8
Add.
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B. 8q 3r for q 2 and r 2
Substitute 2 for q and 2 for r.
8(2) 3(2)
Multiply.
16 6
Subtract.
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Additional Example 3A Physical Science
Application
Use the expression 1.8c 32 to convert the
boiling point temperature from degrees Celsius to
degrees Fahrenheit.
Boiling point of water at sea level 100C
1.8c 32
Substitute 100 for c.
1.8(100) 32
Multiply.
180 32
Add.
212
100C 212F
Water boils at 212F.
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Additional Example 3B Physical Science
Application
Boiling point of water at an altitude of 4400
t meters 85C
1.8c 32
Substitute 85 for c.
1.8(85) 32
Multiply.
153 32
Add.
185
85C 185F
Water boils at 185F at 4400 m.
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Check It Out Example 3A
Convert the temperature from degrees Celsius to
degrees Fahrenheit.
Europes highest recorded temperature
(Seville, Spain) 50C
1.8c 32
Substitute 50 for c.
1.8(50) 32
Multiply.
90 32
Add.
122
50C 122F
The highest recorded temperature in Europe is
122F.
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Check It Out Example 3B
Use the expression 1.8c 32 to convert each
boiling point temperature from degrees Celsius to
degrees Fahrenheit.
10C
1.8c 32
Substitute 10 for c.
1.8(10) 32
Multiply.
18 32
Add.
50
10C 50F
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Lesson Quiz
Evaluate each expression for the given values of
the variables. 1. 6x 9 for x 3 2. x 14
for x 8 3. 4x 3y for x 2, y 3 4. 1.6x
2.9y for x 19, y 6 5. If n is the amount of
money in a savings account, then the expression n
0.03n can be used to find the amount in the
account after it has earned interest for one
year. Find the total in the account after one
year if 500 is the initial amount.
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