Learn to evaluate algebraic expressions.

1-3

Variables and Algebraic Expressions

A variable is a symbol that represents an unknown quantity.

An algebraic expression is an expression that contains numbers, variables, and at least one operation.

​

1-3

Variables and Algebraic Expressions

The multiplication sign is often omitted.

6d 9st mn a3

6 times d 9 times s times t m times n a times a times

The numerical factor of a multiplication expression that contains a variable is called a coefficient. So, 6 is the coefficient of 6d.

1-3

Variables and Algebraic Expressions

Evaluate each expression when x=(-10) and y=2.

• x+y

-10 + 2

-8

Substitute -10 for x and 2 for y.

• xy

-10(2)

-20

1-3

Variables and Algebraic Expressions

Evaluate each expression when x=(-10) and y=2.

1-3

Variables and Algebraic Expressions

When evaluating expressions, use the order of operations.

You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations.

1-3

Variables and Algebraic Expressions

Baseball You plan to divide the 120 players in a baseball league into teams with the same number of players. Use a verbal model to write a variable expression for the number of teams if you know the number of players on each team.

1-3

Variables and Algebraic Expressions

Evaluate the expression for the given value of the variable.

Example B:

4x – 3 for x = 2

4(2) – 3

8 – 3

5

Substitute 2 for x.

Multiply.

Subtract.

1-3

Variables and Algebraic Expressions

Example C:

s ÷ 5 + s, for s = 15

15 ÷ 5 + 15

3 + 15

18

Substitute 15 for s.

Divide.

Add.

Evaluate the expression for the given value of the variable.

1-3

Variables and Algebraic Expressions

5x² + 3x, for x = 2

5(2)² + 3(2)

5(4) + 3(2)

20 + 6

26

Substitute 2 for x.

Evaluate the power.

Multiply.

Add.

Example D:

Evaluate the expression for the given value of the variable.

1-3

Variables and Algebraic Expressions

1.) r ÷ 3 + r, for r = 12

12 ÷ 3 + 12

4 + 12

16

2.) 4y² + 2y, for y = 3

4(3)² + 2(3)

4(9) + 2(3)

36 + 6

42

Substitute 12 for r.

Divide.

Add.

Substitute 3 for y.

Evaluate the power.

Multiply.

Add.

Check your understanding

Evaluate the expression for the given value of the variable.

1-3

Variables and Algebraic Expressions

3.)

Check your understanding:

6

a

+ 4b, for a = 3 and b = 2.

6

a

+ 4b

6

3

+ 4(2)

2 + 8

10

Substitute 3 for a and 2 for b.

Divide and multiply from

left to right.

Add.

1-3

Variables and Algebraic Expressions

Evaluate n + 7 for each value of n.

1. n = 25 2. 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

5. + 3y 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?

38

32

37

162

56

x

23

84

Lesson Quiz

1-3

Variables and Algebraic Expressions

1-3

Variables and Algebraic Expressions

7. Evaluate m + 4 for m = 19.

A. 21

B. 27

C. 23

D. 28

​

1-3

Variables and Algebraic Expressions

8. Evaluate 7x – 8 for x = 5.

A. 20

B. 27

C. 22

D. 32

​

1-3

Variables and Algebraic Expressions

9. Evaluate 6x² + 5x for x = 5.

A. 185

B. 85

C. 175

D. 50

​

1-3

Variables and Algebraic Expressions

10. Evaluate + 5y for x = 3 and y = 5.

A. 38

B. 44

C. 54

D. 64

39

x

1-3

Variables and Algebraic Expressions

11. 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

1-3

Variables and Algebraic Expressions