1. Variables and Expressions
1-1
Variables and Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 3

2. Variables and Expressions
Course 3
1-1
Variables and Expressions
Warm Up
Evaluate.
1. 21  2(3) 15
 9 31
3. 2(9) + (3) 21
4. 6(1.4) + 12
20.4
5. 7(2.9)  5
15.3

3. Variables and Expressions
Course 3
1-1
Variables and Expressions
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
Trees
Price
Maple
Elm
Oak
Dogwood
Crab apple
Birch
$16.99
$22.99
$19.99
$23.99
$26.99
$17.99

4. Variables and Expressions
Course 3
1-1
Variables and Expressions
Learn to evaluate algebraic expressions.

5. Variables and Expressions
Course 3
1-1
Variables and Expressions
Vocabulary
variable
coefficient
algebraic expression
constant
evaluate
substitute

6. Variables and Expressions
Course 3
1-1
Variables and Expressions
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

7. Variables and Expressions
Course 3
1-1
Variables and Expressions
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.

8. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Examples 1A: Evaluating Algebraic Expressions with One Variable
Evaluate each expression for the given value of the variable.
x – 5 for x = 12
12 – 5
Substitute 12 for x. 7
Subtract.

9. Variables and Expressions
Course 3
1-1
Variables and Expressions
Order of Operations
PEMDAS:
1. Parentheses
2. Exponents
3. Multiply and Divide from left to right.
4. Add and Subtract from left to right.
Remember!

10. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Examples 1B: Evaluating Algebraic Expressions with One Variable
Evaluate each expression for the given value of the variable.
2y + 1 for y = 4
2(4) + 1
Substitute 4 for y.
8 + 1
Multiply. 9
Add.

11. Variables and Expressions
Course 3
1-1
Variables and Expressions
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 5 6 7
n Substitute Parentheses Multiply Subtract
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

12. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Examples 1
Evaluate each expression for the given value of the variable.
A. x + 5 for x = 3
3 + 5
Substitute 3 for x. 8
Add.
B. 4c + 1 for c = 11
4(11) + 1
Substitute 11 for c.
44 + 1
Multiply. 45
Add.

13. Variables and Expressions
Course 3
1-1
Variables and Expressions
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 3 4 5
n Substitute Parentheses Multiply Subtract
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

14. Variables and Expressions
Course 3
1-1
Variables and Expressions
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.
8 + 3
Multiply. 11
Add.
B. 9r – 2p for r = 3 and p = 5
9(3) – 2(5)
Substitute 3 for r and 5 for p.
27 – 10
Multiply. 17
Subtract.

15. Variables and Expressions
Course 3
1-1
Variables and Expressions
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.
9 + 8
Multiply. 17
Add.
B. 8q – 3r for q = 2 and r = 2
8(2) – 3(2)
Substitute 2 for q and 2 for r.
16 – 6
Multiply. 10
Subtract.

16. Variables and Expressions
Course 3
1-1
Variables and Expressions
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: 100°C
1.8c + 32
1.8(100) + 32
Substitute 100 for c.
Multiply.
212
Add.
100°C = 212°F
Water boils at 212°F.

17. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Example 3B: Physical Science Application
Boiling point of water at an altitude of t meters: 85°C
1.8c + 32
1.8(85) + 32
Substitute 85 for c.
Multiply.
185
Add.
85°C = 185°F
Water boils at 185°F at 4400 m.

18. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Example 3A
Convert the temperature from degrees Celsius to degrees Fahrenheit.
Europe’s highest recorded temperature (Seville, Spain): 50°C
1.8c + 32
1.8(50) + 32
Substitute 50 for c.
Multiply.
122
Add.
50°C = 122°F
The highest recorded temperature in Europe is 122°F.

19. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Example 3B
Use the expression 1.8c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit.
10°C
1.8c + 32
1.8(10) + 32
Substitute 10 for c.
Multiply. 50
Add.
10°C = 50°F

20. Variables and Expressions
Course 3
1-1
Variables and Expressions
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
x – 2.9y for x = 19, y = 6
5. If n is the amount of money in a savings account, then the expression n n 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. 27 22 17 13
$515