Variables and Expressions 1-1 Variables and Expressions Warm Up Problem of the Day Lesson Presentation Pre-Algebra

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

Try This: Examples 1A and 1B 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.

Try This: Example 1C 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 value 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. 8.5 r – 2p for r = 2 and p = 5.5 8.5(2) – 2(5.5) Substitute 2 for r and 5.5 for p. 17 – 11 Multiply. 6 Subtract.

Try This: Example 2 Evaluate each expression for the given value 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 – 3.5r for q = 2.5 and r = 2 8(2.5) – 3.5(2) Substitute 2.5 for q and 2 for r. 20 – 7 Multiply. 13 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. A. 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 Convert the temperature from degrees Celsius to degrees Fahrenheit. B. Antarctica’s highest recorded temperature (Vanda Station, Scott Coast): 15°C 1.8c + 32 1.8(15) + 32 Substitute 15 for c. 27 + 32 Multiply. 59 Add. 15°C = 59°F The highest recorded temperature in Antarctica is 59°F.

Try This: Example 3A Use the expression 1.8c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit. A. Boiling point of water at an altitude of 4400 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.

Try This: Example 3B Convert the temperature from degrees Celsius to degrees Fahrenheit. B. 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.

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