1-1 Evaluating Algebraic Expressions Warm Up Evaluate. 1. 21 – 2(3) 15 31 21 20.4 15.3 5. 7(2.9) – 5 4. 6(1.4) + 12 3. 2(9) + (3) 2. 4 + 3 9.

1-1 Evaluating Algebraic Expressions

Warm UpEvaluate.

1. 21 – 2(3) 15

31

21

20.4

15.35. 7(2.9) – 5

4. 6(1.4) + 12

3. 2(9) + (3)

2. 4 + 3 9

1-1 Evaluating Algebraic 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?

Trees TreesPrice Price

Maple

Elm

Oak

Dogwood

Crab apple

Birch

$16.99

$22.99

$19.99

$23.99

$26.99

$17.99

$337.90

1-1 Evaluating Algebraic Expressions

Learn to evaluate algebraic expressions.

1-1 Evaluating Algebraic Expressions

Vocabularyvariablecoefficientalgebraic expressionconstantevaluatesubstitute

1-1 Evaluating Algebraic 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

1-1 Evaluating Algebraic Expressions

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.

An algebraic expression has one or more variables.

1-1 Evaluating Algebraic Expressions

Evaluate each expression for the given value of the variable.

Additional Example 1A: Evaluating Algebraic Expressions with One Variable

Substitute 12 for x.

Subtract.

x – 5 for x = 12

12 – 5

7

1-1 Evaluating Algebraic Expressions

Order of Operations

PEMDAS: 1. Parentheses 2. Exponents3. Multiply and Divide from left to right.4. Add and Subtract from left to right.

Remember!

1-1 Evaluating Algebraic Expressions

Evaluate each expression for the given value of the variable.

Additional Example 1B: Evaluating Algebraic Expressions with One Variable

Substitute 4 for y.

Multiply.

2y + 1 for y = 4

2(4) + 1

8 + 1

Add.9

1-1 Evaluating Algebraic Expressions

Evaluate the expression for the given values of the variable.

Additional Example 1C: Evaluating Algebraic Expressions with One 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

1-1 Evaluating Algebraic Expressions

Evaluate each expression for the given value of the variable.

Check It Out: Examples 1

Substitute 3 for x.

Add.

A. x + 5 for x = 3

3 + 5

8

Substitute 11 for c.

Multiply.

B. 4c + 1 for c = 11

4(11) + 1

44 + 1

Add.45

1-1 Evaluating Algebraic Expressions

Evaluate the expression for the given values of the variable.

Check It Out: Example 1

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

1-1 Evaluating Algebraic Expressions

Evaluate each expression for the given values of the variables.

Additional Example 2: Evaluating Algebraic Expressions with Two Variables

Substitute 2 for x and 1 for y.

Multiply.

A. 4x + 3y for x = 2 and y = 1

4(2) + 3(1)

8 + 3

Substitute 3 for r and 5 for p.

Multiply.

B. 9r – 2p for r = 3 and p = 5

9(3) – 2(5)

27 – 10

Add.11

Subtract.17

1-1 Evaluating Algebraic Expressions

Evaluate each expression for the given values of the variables.

Check It Out: Example 2

Substitute 3 for x and 4 for y.

Multiply.

A. 3x + 2y for x = 3 and y = 4

3(3) + 2(4)

9 + 8

Substitute 2 for q and 2 for r.

Multiply.

B. 8q – 3r for q = 2 and r = 2

8(2) – 3(2)

16 – 6

Add.17

Subtract.10

1-1 Evaluating Algebraic Expressions

Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit.

Additional Example 3A: Physical Science Application

Substitute 100 for c.

Multiply.

Boiling point of water at sea level: 100°C

1.8(100) + 32

180 + 32

1.8c + 32

Add.212

100°C = 212°F

Water boils at 212°F.

1-1 Evaluating Algebraic Expressions

Additional Example 3B: Physical Science Application

Substitute 85 for c.

Multiply.

Boiling point of water at an altitude of 4400 t meters: 85°C

1.8(85) + 32

153 + 32

1.8c + 32

Add.185

85°C = 185°F

Water boils at 185°F at 4400 m.

1-1 Evaluating Algebraic Expressions

Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit.

Check It Out: Example 3A

Substitute 50 for c.

Multiply.

Europe’s highest recorded temperature (Seville, Spain): 50°C

1.8(50) + 32

90 + 32

1.8c + 32

Add.122

50°C = 122°F

The highest recorded temperature in Europe is 122°F.

1-1 Evaluating Algebraic Expressions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-1 Evaluating Algebraic Expressions

Lesson QuizEvaluate 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.

27

22

17

13

$515