EXAMPLE 1 Evaluate expressions Evaluate the expression 27

EXAMPLE 1 Evaluate expressions Evaluate the expression 27 32 2 – 3. STEP 1 There are no grouping symbols, so go to Step 2. STEP 2 Evaluate powers. 27 32 2 – 3 = 27 9 2– 3 Evaluate power. STEP 3 Multiply and divide from left to right. 27 9 2 – 3 = 3 2 – 3 Divide. 3 2– 3 =6– 3 Multiply.

EXAMPLE 1 Evaluate expressions STEP 4 Add and subtract from left to right. 6– 3=3 Subtract. ANSWER The value of the expression 27 32 2 – 3 is 3.

GUIDED PRACTICE 1. for Example 1 Evaluate the expression 20 – 42 ANSWER 1. 4 2. Evaluate the expression 2 32 + 4 ANSWER 2. 22 3. Evaluate the expression 32 ANSWER 3. 10 23 + 6

GUIDED PRACTICE 4. Evaluate the expression 15 + 62 – 4 ANSWER 4. for Example 1 47

EXAMPLE 2 Evaluate expressions with grouping symbols Evaluate the expression. a. 7(13 – 8) = 7(5) = 35 Subtract within parentheses. Multiply. b. 24 – (32 + 1) = 24 – (9 + 1) = 24 – 10 = 14 Evaluate power. Add within parentheses. Subtract. c. 2[30 – (8 + 13)] = 2[30 – 21] Add within parentheses. Subtract within brackets. = 2[9] Multiply. = 18

EXAMPLE 3 Evaluate an algebraic expression Evaluate the expression when x = 4. 9 4 9 x = 3(4 + 2) 3(x + 2) Substitute 4 for x. = 9 4 3 6 = 36 18 Multiply. = 2 Divide. Add within parentheses.

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression. 5. 4(3 + 9) = 48 6. 3(8 – 22) = 12 7. 2[( 9 + 3) 4] =6

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when y = 8. 8. y 2 – 3 = 61 9. 12 – y – 1 = 3 10. 10 y + 1 = 9 y+1

EXAMPLE 4 Standardized Test Practice

EXAMPLE 4 SOLUTION 12(3 j +2 s) + 30 = 12(3 1. 25 + 2 2) + 30 Substitute 1. 25 for j and 2 for s. = 12(3. 75 + 4) + 30 Multiply within parentheses. = 12(7. 75) + 30 Add within parentheses. = 93 + 30 Multiply. = 123 Add. ANSWER The sponsor’s cost is $123. The correct answer D. is B. A C B

GUIDED PRACTICE for Example 4 11. WHAT IF? In Example 4, suppose the number of volunteers doubles. Does the sponsor’s cost double as well? Explain. ANSWER The sponsor’s cost is $216. No; the total cost of the juice drinks and sandwiches will double, but the cost of the trash bags will not.