Download 1 Evaluate an expression containing variables by substituting

1-1 Variables and Expressions
Vocabulary
Evaluate an expression containing
variables by substituting rational
numbers for the variables.
variable
coefficient
algebraic expression
constant
evaluate
substitute
Pre-Algebra
A variable is a letter that represents a value
that can change or vary.
The coefficient is the number multiplied
by the variable.
Coefficient
An algebraic expression has one or more
variables.
In the algebraic expression x + 6, 6 is a
constant because it does not change.
Variable
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 Example 1C: Evaluating Algebraic
Expressions with One Variable
Additional Examples 1A and 1B: Evaluating Algebraic
Expressions with One Variable
Evaluate each expression for the given value
of the variable.
Evaluate the expression for the given values
of the variable.
A. x – 5 for x = 12
Substitute 12 for x.
12 – 5
Subtract.
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C. 6(n + 2) – 4 for n = 5, 6, 7
B. 2y + 1 for y = 4
Substitute 4 for y.
2(4) + 1
Multiply.
8+1
Add.
9
Additional Example 2: Evaluating Algebraic
Expressions with Two Variables
Evaluate each expression for the given value
of the variables.
A. 4x + 3y for x = 2 and y = 1
4(2) + 3(1)
8+3
11
Substitute 2 for x and 1 for y.
Multiply.
Add.
B. 8.5 r – 2p for r = 2 and p = 5.5
Substitute 2 for r and 5.5 for p.
8.5(2) – 2(5.5)
Multiply.
17 – 11
Subtract.
6
n
Substitute
Parentheses
Multiply
Subtract
5 6(5 + 2) – 4
6(7) – 4
42 – 4
38
6 6(6 + 2) – 4
6(8) – 4
48 – 4
44
7 6(7 + 2) – 4
6(9) – 4
54 – 4
50
Additional Example 3A: Physical Science Application
Use the expression 1.8c + 32 to convert the
boiling point temperature from degrees
Celsius to degrees Fahrenheit.
A. Boiling point of water at sea level: 100°C
1.8c + 32
1.8(100) + 32
180 + 32
Substitute 100 for c.
Multiply.
Add.
212
100°C = 212°F
Water boils at 212°F.
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Additional Example 3B: Physical Science Application
Convert the temperature from degrees Celsius
to degrees Fahrenheit.
B. Antarctica’s highest recorded temperature
(Vanda Station, Scott Coast): 15°C
1.8c + 32
Substitute 15 for c.
1.8(15) + 32
Multiply.
27 + 32
Add.
59
15°C = 59°F
The highest recorded temperature in Antarctica is 59°F.
Try This: Examples 1A and 1B
Evaluate each expression for the given value
of the variable.
A. x + 5 for x = 3
3+5
8
Try This: Example 2
Evaluate the expression for the given values
of the variable.
C. 5(n + 3) – 2 for n = 3, 4, 5
Substitute
Parentheses
Add.
B. 4c + 1 for c = 11
Substitute 11 for c.
4(11) + 1
Multiply.
44 + 1
Add.
45
Try This: Example 1C
n
Substitute 3 for x.
Multiply
Subtract
3 5(3 + 3) – 2
5(6) – 2
30 – 2
28
4 5(4 + 3) – 2
5(7) – 2
35 – 2
33
5 5(5 + 3) – 2
5(8) – 2
40 – 2
38
Evaluate each expression for the given value
of the variables.
A. 3x + 2y for x = 3 and y = 4
3(3) + 2(4)
9+8
17
Substitute 3 for x and 4 for y.
Multiply.
Add.
B. 8q – 3.5r for q = 2.5 and r = 2
Substitute 2.5 for q and 2 for r.
8(2.5) – 3.5(2)
Multiply.
20 – 7
Subtract.
13
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Try This: Example 3A
Use the expression 1.8c + 32 to convert each
boiling point temperature from degrees
Celsius to degrees Fahrenheit.
A. Boiling point of water at an altitude of
4400 meters: 85°C
1.8c + 32
Substitute 85 for c.
1.8(85) + 32
Multiply.
153 + 32
Add.
185
85°C = 185°F
Water boils at 185°F at 4400 m.
Try This: Example 3B
Convert the temperature from degrees Celsius
to degrees Fahrenheit.
B. Europe’s highest recorded temperature
(Seville, Spain): 50°C
1.8c + 32
Substitute 50 for c.
1.8(50) + 32
Multiply.
90 + 32
Add.
122
50°C = 122°F
The highest recorded temperature in
Europe is 122°F.
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