1. Warm Up Evaluate. 1. 21  2(3) 15 31 21 20.4 15.3 Course 3 1-1 Variables and Expressions 5. 7(2.9)  5 4. 6(1.4) + 12 3. 2(9) + (3) 2. 4 + 3  9

2. 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 Price Maple Elm Oak Dogwood Crab apple Birch $16.99 $22.99 $19.99 $23.99 $26.99 $17.99 $337.90 Course 3 1-1 Variables and Expressions

3. Learn to evaluate algebraic expressions. Course 3 1-1 Variables and Expressions

4. Vocabulary variable coefficient algebraic expression constant evaluate substitute Course 3 1-1 Variables and Expressions

5. A variable is a letter that represents a value that can change or vary. The coefficient is the number multiplied by the variable. CoefficientVariable Course 3 1-1 Variables and Expressions

6. 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 1-1 Variables and Expressions An algebraic expression has one or more variables.

7. Evaluate each expression for the given value of the variable. Additional Examples 1A: Evaluating Algebraic Expressions with One Variable Substitute 12 for x. Subtract. x – 5 for x = 12 12 – 5 Course 3 1-1 Variables and Expressions 7

8. Course 3 1-1 Variables and Expressions 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!

9. Evaluate each expression for the given value of the variable. Additional Examples 1B: Evaluating Algebraic Expressions with One Variable Course 3 1-1 Variables and Expressions Substitute 4 for y. Multiply. 2y + 1 for y = 4 2(4) + 1 8 + 1 Add. 9

10. 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 Course 3 1-1 Variables and Expressions 567567 n Substitute Parentheses Multiply Subtract 6(5 + 2) – 46(7) – 4 42 – 4 38 6(6 + 2) – 46(8) – 4 48 – 4 44 6(7 + 2) – 46(9) – 4 54 – 4 50

11. 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 Course 3 1-1 Variables and Expressions 8 Substitute 11 for c. Multiply. B. 4c + 1 for c = 11 4(11) + 1 44 + 1 Add. 45

12. 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 1-1 Variables and Expressions 345345 n Substitute Parentheses Multiply Subtract 5(3 + 3) – 25(6) – 2 30 – 2 28 5(4 + 3) – 25(7) – 2 35 – 2 33 5(5 + 3) – 25(8) – 2 40 – 2 38

13. 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) Course 3 1-1 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

14. 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 1-1 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

15. Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit. Additional Example 3A: Physical Science Application Course 3 1-1 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.

16. Additional Example 3B: Physical Science Application Course 3 1-1 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.

17. Convert the temperature from degrees Celsius to degrees Fahrenheit. Check It Out: Example 3A Course 3 1-1 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.

18. Use the expression 1.8c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit. Check It Out: Example 3B Course 3 1-1 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

19. Lesson Quiz 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 Course 3 1-1 Variables and Expressions