Variables and Expressions 1-1 Variables and Expressions Warm Up Problem of the Day Lesson Presentation Course 3

Variables and Expressions Course 3 1-1 Variables and Expressions 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

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

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

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

Variables and Expressions Course 3 1-1 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

Variables and Expressions Course 3 1-1 Variables and Expressions 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.

Variables and Expressions Course 3 1-1 Variables and Expressions Additional Examples 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.

Variables and Expressions 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!

Variables and Expressions Course 3 1-1 Variables and Expressions Additional Examples 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.

Variables and Expressions Course 3 1-1 Variables and Expressions 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

Variables and Expressions Course 3 1-1 Variables and Expressions 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.

Variables and Expressions Course 3 1-1 Variables and Expressions 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

Variables and Expressions Course 3 1-1 Variables and Expressions 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.

Variables and Expressions Course 3 1-1 Variables and Expressions 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.

Variables and Expressions Course 3 1-1 Variables and Expressions 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.

Variables and Expressions Course 3 1-1 Variables and Expressions 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.

Variables and Expressions Course 3 1-1 Variables and Expressions Check It Out: Example 3A 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.

Variables and Expressions Course 3 1-1 Variables and Expressions Check It Out: Example 3B Use the expression 1.8c + 32 to convert each boiling point 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

Variables and Expressions Course 3 1-1 Variables and Expressions 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