1. Warm Up Problem of the Day Lesson Presentation 1-7 Variables and Algebraic Expressions Course 2

2. Warm Up Evaluate. 1. 5(7) – 1 2. 7(18 – 11) 3. 22 + 17  8 + 3 4. 36 + 15(40 – 35) 5. 3 3 + 7(12 – 4) 34 49 161 111 83

3. Problem of the Day If charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12? $28

4. Learn to evaluate algebraic expressions.

5. Vocabulary variable constant algebraic expression evaluate

6. Ron Howard was born in 1954. You can find out what year Ron turned 16 by adding the year he was born to his age. 1954 + 16 In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be 1954 + a.

7. 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, 1954 + a is an algebraic expression for the year Ron Howard turns a certain age.

8. To evaluate an algebraic expression, substitute a number for the variable. 1954 + a a 1990 1954 + 36 36 1975 1954 + 21 21 1972 1954 + 18 18 1970 1954 + 16 16 Year born + age = year at age Age

9. Evaluate k + 9 for each value of k . Additional Example 1: Evaluating Algebraic Expressions A. k = 5 k + 9 5 + 9 14 Substitute 5 for k. Add. B. k = 2 k + 9 2 + 9 Substitute 2 for k. 11 Add.

10. Check It Out: Example 1 Evaluate a + 6 for each value of a . A. a = 3 a + 6 3 + 6 9 Substitute 3 for a. Add. B. a = 5 a + 6 5 + 6 Substitute 5 for a. 11 Add.

11. Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.

12. Evaluate the expression for the given value of the variable. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations A. 4 x – 3 for x = 2 4( 2 ) – 3 8 – 3 5 Substitute 2 for x. Multiply. Subtract.

13. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 3 + 15 18 C. 5 x 2 + 3 x , for x = 2 5( 2 ) 2 + 3( 2 ) 5(4) + 3(2) 20 + 6 26 Substitute 15 for s. Divide. Add. Substitute 2 for x. Evaluate the power. Multiply. Add.

14. Check It Out: Example 2A Evaluate the expression for the given value of the variable. A. 3 x – 2 for x = 3 3( 3 ) – 2 9 – 2 7 Substitute 3 for x. Multiply. Subtract.

15. Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 4 + 12 16 C. 4 y 2 + 2 y , for y = 3 4( 3 ) 2 + 2( 3 ) 4(9) + 2(3) 36 + 6 42 Substitute 12 for r. Divide. Add. Substitute 3 for y. Evaluate the power. Multiply. Add.

16. Evaluate Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6 a + 4 b , for a = 3 and b = 2 . 6 a + 4 b 6 3 + 4( 2 ) 2 + 8 10 Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add.

17. Check It Out: Example 3 Evaluate 8 w + 2 x , for w = 4 and x = 2 . 8 w + 2 x 8 4 + 2( 2 ) 2 + 4 6 Substitute 4 for w and 2 for x. Divide and multiply from left to right. Add.

18. Lesson Quiz Evaluate n + 7 for each value of n . 1. n = 25 2. n =31 Evaluate each algebraic expression for the given value of the variables 3. 6 y – 5 for y = 7 4. 4 x 2 + 3 x for x = 6 5. + 3 y for x = 4 and y = 3 6. The expression 7 d gives the number of days in d weeks. Evaluate 7 d for d = 12. How many days are in 12 weeks? 38 32 37 162 56 x 23 84