6Harrison Ford was born in 1942 Harrison Ford was born in You can find out what year Harrison turned 18 by adding the year he was born to his age.In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Harrison Ford’s age. When he turns a years old, the year will bea.
7The letter a has a value that can change, or vary The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change.An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, a is an algebraic expression for the year Ron Howard turns a certain age.
8Year born + age = year at age 161970181972211975361990aaTo evaluate an algebraic expression, substitute a number for the variable.
9Additional Example 1: Evaluating Algebraic Expressions Evaluate k + 9 for each value of k.A. k = 5k + 95 + 9Substitute 5 for k.14Add.B. k = 2k + 92 + 9Substitute 2 for k.11Add.
10Check It Out: Example 1Evaluate a + 6 for each value of a.A. a = 3a + 63 + 6Substitute 3 for a.9Add.B. a = 5a + 65 + 6Substitute 5 for a.11Add.
11Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.
12Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations Evaluate the expression for the given value of the variable.A. 4x – 3 for x = 24(2) – 3Substitute 2 for x.Multiply.8 – 35Subtract.
13Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 1515 ÷Substitute 15 for s.3 + 15Divide.18Add.C. 5x2 + 3x, for x = 25(2)2 + 3(2)Substitute 2 for x.5(4) + 3(2)Evaluate the power.20 + 6Multiply.26Add.
14Check It Out: Example 2AEvaluate the expression for the given value of the variable.A. 3x – 2 for x = 33(3) – 2Substitute 3 for x.Multiply.9 – 2Subtract.7
15Check It Out: Example 2B. r ÷ 3 + r, for r = 1212 ÷Substitute 12 for r.4 + 12Divide.16Add.C. 4y2 + 2y, for y = 34(3)2 + 2(3)Substitute 3 for y.4(9) + 2(3)Evaluate the power.36 + 6Multiply.42Add.
16Substitute 3 for a and 2 for b. + 4(2) Additional Example 3: Evaluating Algebraic Expressions with Two Variables6aEvaluate+ 4b, for a = 3 and b = 2.6a+ 4b63Substitute 3 for a and 2 for b.+ 4(2)Divide and multiply fromleft to right.2 + 810Add.
17Substitute 4 for w and 2 for x. Check It Out: Example 38wEvaluate+ 2x, for w = 4 and x = 2.8w+ 2x84+ 2(2)Substitute 4 for w and 2 for x.Divide and multiply fromleft to right.2 + 46Add.
18Lesson QuizzesStandard Lesson QuizLesson Quiz for Student Response Systems
19Evaluate n + 7 for each value of n. 1. n = 25 2. n =31 Lesson QuizEvaluate n + 7 for each value of n.1. n = n =31Evaluate each algebraic expression for the given value of the variables3. 6y – 5 for y = 74. 4x2 + 3x for x = 6y for x = 4 and y = 36. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks?32383716256x2384