Page 175 - Basic College Mathematics with Early Integers

152 C HAPTE R 2 I INTEGERS AND INTRODUCTION TO VARIABLES

PRACTICE 10 Example 10 Simplify: -23-3 + 21-1 + 6)4 - 5
Simplify:
-43-2 + 51-3 + 524 - 7 Solution: Here we begin with the innermost set of parentheses.
-23-3 + 21-1 + 624 - 5 =-23-3 + 21524 - 5 Write -1 + 6 as 5.

=-23-3 + 104 - 5 Multiply.
=-2172 - 5 Add.
=-14 - 5 Multiply.
=-19 Subtract.
Work Practice 10

Concept Check True or false? Explain your answer.The result of

-413 - 72 - 819 - 62

is positive because there are four negative signs.

Objective Evaluating Expressions

Now we practice evaluating expressions.

PRACTICE 11 Example 11 Evaluate x 2 and -x 2 for x =-11.
Evaluate x 2 and -x 2 for 2 2
x =-12 . Solution: x = 1-112 = 1-1121-112 = 121
2
2
-x =-1-112 =-1-1121-112 =-121
Work Practice 11

PRACTICE 12 Example 12 Evaluate 6z 2 for z = 2 and z =-2.
Evaluate 5y 2 for y = 3 and
2
2
y =-3. Solution: 6z = 6122 = 6142 = 24
2
2
6z = 61-22 = 6142 = 24
Work Practice 12

PRACTICE 13 Example 13 Evaluate x + 2y - z for x = 3 and y =-5 and z =-4.
2
Evaluate x + y - z for Solution: Replace x with 3, y with -5, z with -4 and simplify.
x =-5, y =-2 , and
z = 30.
Remember to rewrite the subtraction sign.

x+2y-z=3+2(–5)-(–4) Let x = 3, y =-5, and z =-4.
=3+(–10)+4 Replace 21-52 with its product, -10.
Answers
=–3 Add.
10. -39 11. 144; -144 12. 45; 45 Copyright 2012 Pearson Education, Inc.
13. -7 Work Practice 13

Concept Check Answer
false; -413 - 72 - 819 - 62 =-8