1. Warm Up
Evaluate.
1. 5(7) – 1
2. 7(18 – 11)
 8 + 3
(40 – 35)
(12 – 4) 34 49
161
111 83

2. Problem of the Day
If charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12?
$28

3. Learn to evaluate algebraic expressions.

4. Vocabulary
variable
constant
algebraic expression
evaluate

5. Harrison Ford was born in 1942
Harrison Ford was born in You can find out what year Harrison turned 18 by adding the year he was born to his age.
In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Harrison Ford’s age. When he turns a years old, the year will be a.

6. The letter a has a value that can change, or vary
The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change.
An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, a is an algebraic expression for the year Ron Howard turns a certain age.

7. Year born + age = year at age16
1970 18
1972 21
1975 36
1990 a a
To evaluate an algebraic expression, substitute a number for the variable.

8. Additional Example 1: Evaluating Algebraic Expressions
Evaluate k + 9 for each value of k.
A. k = 5
k + 9
5 + 9
Substitute 5 for k. 14
Add.
B. k = 2
k + 9
2 + 9
Substitute 2 for k. 11
Add.

9. Check It Out: Example 1
Evaluate a + 6 for each value of a.
A. a = 3
a + 6
3 + 6
Substitute 3 for a. 9
Add.
B. a = 5
a + 6
5 + 6
Substitute 5 for a. 11
Add.

10. Multiplication and division of variables can be written in several ways, as shown in the table.
When evaluating expressions, use the order of operations.

11. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations
Evaluate the expression for the given value of the variable.
A. 4x – 3 for x = 2
4(2) – 3
Substitute 2 for x.
Multiply.
8 – 3 5
Subtract.

12. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations
B. s ÷ 5 + s, for s = 15
15 ÷
Substitute 15 for s.
3 + 15
Divide. 18
Add.
C. 5x2 + 3x, for x = 2
5(2)2 + 3(2)
Substitute 2 for x.
5(4) + 3(2)
Evaluate the power.
20 + 6
Multiply. 26
Add.

13. Check It Out: Example 2A
Evaluate the expression for the given value of the variable.
A. 3x – 2 for x = 3
3(3) – 2
Substitute 3 for x.
Multiply.
9 – 2
Subtract. 7

14. Check It Out: Example 2
B. r ÷ 3 + r, for r = 12
12 ÷
Substitute 12 for r.
4 + 12
Divide. 16
Add.
C. 4y2 + 2y, for y = 3
4(3)2 + 2(3)
Substitute 3 for y.
4(9) + 2(3)
Evaluate the power.
36 + 6
Multiply. 42
Add.

15. Substitute 3 for a and 2 for b. + 4(2)
Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6 a
Evaluate
+ 4b, for a = 3 and b = 2. 6 a
+ 4b 6 3
Substitute 3 for a and 2 for b.
+ 4(2)
Divide and multiply from
left to right.
2 + 8 10
Add.

16. Substitute 4 for w and 2 for x.
Check It Out: Example 3 8 w
Evaluate
+ 2x, for w = 4 and x = 2. 8 w
+ 2x 8 4
+ 2(2)
Substitute 4 for w and 2 for x.
Divide and multiply from
left to right.
2 + 4 6
Add.

17. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

18. Evaluate n + 7 for each value of n. 1. n = 25 2. n =31
Lesson Quiz
Evaluate n + 7 for each value of n.
1. n = n =31
Evaluate each algebraic expression for the given value of the variables
3. 6y – 5 for y = 7
4. 4x2 + 3x for x = 6
y for x = 4 and y = 3
6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? 32 38 37
162 56 x 23 84

19. Lesson Quiz for Student Response Systems
1. Evaluate m + 4 for m = 19.
A. 21
B. 27
C. 23
D. 28

20. Lesson Quiz for Student Response Systems
2. Evaluate 7x – 8 for x = 5.
A. 20
B. 27
C. 22
D. 32

21. Lesson Quiz for Student Response Systems
3. Evaluate 6x2 + 5x for x = 5.
A. 185
B. 85
C. 175
D. 50

22. Lesson Quiz for Student Response Systems39 y
4. Evaluate y for x = 3 and y = 5.
A. 38
B. 44
C. 54
D. 64

23. Lesson Quiz for Student Response Systems
5. The expression 12n gives the number of months in n years. Evaluate 12n for n = 3. How many months are in 3 years?
A. 12 months
B. 24 months
C. 36 months
D. 48 months