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1-1 Variables and Expressions Vocabulary Evaluate an expression containing variables by substituting rational numbers for the variables. variable coefficient algebraic expression constant evaluate substitute Pre-Algebra A variable is a letter that represents a value that can change or vary. The coefficient is the number multiplied by the variable. Coefficient An algebraic expression has one or more variables. In the algebraic expression x + 6, 6 is a constant because it does not change. Variable To evaluate an algebraic expression, substitute a given number for the variable, and find the value of the resulting numerical expression. 1 Additional Example 1C: Evaluating Algebraic Expressions with One Variable Additional Examples 1A and 1B: Evaluating Algebraic Expressions with One Variable Evaluate each expression for the given value of the variable. Evaluate the expression for the given values of the variable. A. x – 5 for x = 12 Substitute 12 for x. 12 – 5 Subtract. 7 C. 6(n + 2) – 4 for n = 5, 6, 7 B. 2y + 1 for y = 4 Substitute 4 for y. 2(4) + 1 Multiply. 8+1 Add. 9 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) 8+3 11 Substitute 2 for x and 1 for y. Multiply. Add. B. 8.5 r – 2p for r = 2 and p = 5.5 Substitute 2 for r and 5.5 for p. 8.5(2) – 2(5.5) Multiply. 17 – 11 Subtract. 6 n Substitute Parentheses Multiply Subtract 5 6(5 + 2) – 4 6(7) – 4 42 – 4 38 6 6(6 + 2) – 4 6(8) – 4 48 – 4 44 7 6(7 + 2) – 4 6(9) – 4 54 – 4 50 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) + 32 180 + 32 Substitute 100 for c. Multiply. Add. 212 100°C = 212°F Water boils at 212°F. 2 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 Substitute 15 for c. 1.8(15) + 32 Multiply. 27 + 32 Add. 59 15°C = 59°F The highest recorded temperature in Antarctica is 59°F. Try This: Examples 1A and 1B Evaluate each expression for the given value of the variable. A. x + 5 for x = 3 3+5 8 Try This: Example 2 Evaluate the expression for the given values of the variable. C. 5(n + 3) – 2 for n = 3, 4, 5 Substitute Parentheses Add. B. 4c + 1 for c = 11 Substitute 11 for c. 4(11) + 1 Multiply. 44 + 1 Add. 45 Try This: Example 1C n Substitute 3 for x. Multiply Subtract 3 5(3 + 3) – 2 5(6) – 2 30 – 2 28 4 5(4 + 3) – 2 5(7) – 2 35 – 2 33 5 5(5 + 3) – 2 5(8) – 2 40 – 2 38 Evaluate each expression for the given value of the variables. A. 3x + 2y for x = 3 and y = 4 3(3) + 2(4) 9+8 17 Substitute 3 for x and 4 for y. Multiply. Add. B. 8q – 3.5r for q = 2.5 and r = 2 Substitute 2.5 for q and 2 for r. 8(2.5) – 3.5(2) Multiply. 20 – 7 Subtract. 13 3 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 Substitute 85 for c. 1.8(85) + 32 Multiply. 153 + 32 Add. 185 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 Substitute 50 for c. 1.8(50) + 32 Multiply. 90 + 32 Add. 122 50°C = 122°F The highest recorded temperature in Europe is 122°F. 4