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

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

Learn to evaluate algebraic expressions.

Vocabulary variable coefficient algebraic expression constant evaluate substitute

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

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.

Additional Example 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.

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!

Additional Example 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.

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

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.

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

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.

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.

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. 180 + 32 Multiply. 212 Add. 100°C = 212°F Water boils at 212°F.

Additional Example 3B: Physical Science Application Boiling point of water at an altitude of 4400 t meters: 85°C 1.8c + 32 1.8(85) + 32 Substitute 85 for c. 153 + 32 Multiply. 185 Add. 85°C = 185°F Water boils at 185°F at 4400 m.

Check It Out: Example 3A Use the expression 1.8c + 32 to 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. 90 + 32 Multiply. 122 Add. 50°C = 122°F The highest recorded temperature in Europe is 122°F.

Check It Out: Example 3B Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. 10°C 1.8c + 32 1.8(10) + 32 Substitute 10 for c. 18 + 32 Multiply. 50 Add. 10°C = 50°F

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz 1. 6x + 9 for x = 3 2. x + 14 for x = 8 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 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

Lesson Quiz for Student Response Systems 1. Evaluate the expression for the given value of the variable. 6x + 12 for x = 7 A. 23 B. 40 C. 54 D. 65

Lesson Quiz for Student Response Systems 2. Evaluate the expression for the given value of the variable. k + 72 for k = 7 A. 79 B. 82 C. 96 D. 98

Lesson Quiz for Student Response Systems 3. Evaluate the expression for the given values of the variables. 2m + 2n for m = 4, n = 5 A. 18 B. 20 C. 22 D. 24

Lesson Quiz for Student Response Systems 4. Evaluate the expression for the given values of the variables. 3.2r – 4.6s for r = 20, s = 5 A. 30 B. 35 C. 39 D. 41

Lesson Quiz for Student Response Systems 5. If n is the amount of money that Bill had borrowed from a bank, then the expression n + 0.05n can be used to find the total amount Bill has to return after one year with respect to the interest rate. How much money should Bill pay after one year if $700 is the amount borrowed? A. $710 B. $717 C. $735 D. $742