A1.b How Do I Simplify and Evaluate Algebraic Expressions?

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpEvaluate.

1. 21 2(3) 15

31

21

20.4

15.3

Course 3

A1.b How Do I Simplify and Evaluate Algebraic Expressions?

5. 7(2.9) 5

4. 6(1.4) + 12

3. 2(9) + (3)

2. 4 + 3 9

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

DogwoodCrab apple

Birch

$16.99

$22.99

$19.99

$23.99

$26.99

$17.99

$337.90

Course 3

A1.b Variables and Expressions

Learn to evaluate algebraic expressions.

Course 3

A1.b Variables and Expressions

Vocabularyvariablecoefficientalgebraic expressionconstantevaluatesubstitute

Course 3

A1.b 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

Course 3

A1.b Variables and 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.

Course 3

A1.a Variables and Expressions

An algebraic expression has one or more variables.

Evaluate each expression for the given value of the variable.

Example 1A: Evaluating Algebraic Expressions with One Variable

Substitute 12 for x.

Subtract.

x – 5 for x = 12

12 – 5

Course 3

A1.a Variables and Expressions

7

Course 3

A1.a Variables and 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!

Evaluate each expression for the given value of the variable.

Example 1B: Evaluating Algebraic Expressions with One Variable

Course 3

A1.a Variables and Expressions

Substitute 4 for y.

Multiply.

2y + 1 for y = 4

2(4) + 1

8 + 1

Add.9

Evaluate the expression for the given values of the variable.

Example 1C: Evaluating Algebraic Expressions with One Variable

6(n + 2) – 4 for n = 5, 6, 7

Course 3

A1.b Variables and Expressions

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

Evaluate each expression for the given value of the variable.

Check It Out: Example 1

Substitute 3 for x.

Add.

A. x + 5 for x = 3

3 + 5

Course 3

A1.a Variables and Expressions

8

Substitute 11 for c.

Multiply.

B. 4c + 1 for c = 11

4(11) + 1

44 + 1

Add.45

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

Course 3

A1.a Variables and Expressions

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

Evaluate each expression for the given values of the variables.

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)

Course 3

A1.a Variables and Expressions

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

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)

Course 3

A1.a Variables and Expressions

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

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

Example 3A: Physical Science Application

Course 3

A1.b Variables and Expressions

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.

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

Check It Out: Example 3A

Course 3

A1.b Variables and Expressions

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.

Example 3B: Physical Science Application

Course 3

A1.b Variables and Expressions

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.

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

Check It Out: Example 3B

Course 3

A1.b Variables and Expressions

Substitute 10 for c.

Multiply.

10°C

1.8(10) + 32

18 + 32

1.8c + 32

Add.50

10°C = 50°F

Lesson QuizEvaluate each expression for the given values of the variables.

1. 6x + 9 for x = -3

2. -2x – 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.

-9

-30

17

13

$515Course 3

A1.b Variables and Expressions