Page 142 - Basic College Mathematics with Early Integers

S E C T I O N 2.2 I INTRODUCTION TO INTEGERS 119

In general, we have the following:

Opposites
If a is a number, then -1-a2 = a.

Notice that because “the opposite of” is written as “ ”, to find the opposite of a-
number, we place a “ ” sign in front of the number.-

Example 5 Find the opposite of each number. PRACTICE 5
Find the opposite of each
a. 11 b. -2 c. 0 number.

Solution: a. 7 b. -17
Remember
a. The opposite of 11 is -11.
that 0 is neither positive
b. The opposite of -2 is -1-22 or 2.
nor negative.
c. The opposite of 0 is 0.
Work Practice 5

Concept Check True or false? The number 0 is the only number that is its
own opposite.

Example 6 Simplify. PRACTICE 6

Simplify.
a. -1-42 b. - ƒ -5 ƒ c. - ƒ 6 ƒ
a. - ƒ -2 ƒ b. - ƒ 5 ƒ
Solution: c. -1-112
a. -1-42 = 4 The opposite of negative 4 is 4.

b. ––5=–5 The opposite of the absolute value of -5 is the
opposite of 5, or -5.
c. –6=–6 The opposite of the absolute value of 6 is the
opposite of 6, or -6.
Work Practice 6

Example 7 Evaluate - ƒ -x ƒ if x =-2. PRACTICE 7

Evaluate - ƒ x ƒ if x =-9.
Solution: Carefully replace x with -2; then simplify.
- ƒ -x ƒ =- ƒ -1-22 ƒ Replace x with -2.
then ––(–2)=–2=–2.

Work Practice 7
Answers
5. a. -7 b. 17
6. a. -2 b. -5 c. 11
7. -9

Concept Check Answer
True