Intermediate Algebra (11th edition)

SECTION 1.1 Basic Concepts 7

Absolute Value

For any real number a, ae

a

a

if a is positive or 0

if a is negative.

The formal definition of absolute value follows.

CAUTION Because absolute value represents distance, and distance is never

negative, the absolute value of a number is always positive or 0.

Distance is 5,

so ⏐–5⏐ = 5.

Distance is 5,

so ⏐ (^5) ⏐ = 5.
–5 0 5
FIGURE 7
NOW TRY
EXERCISE 5
Simplify by finding each
absolute value.
(a) (b)
(c)| 4 |-|- 4 |

|- 7 | -|- 15 |

The second part of this definition, if ais negative, requires careful thought.

If ais a negativenumber, then the additive inverse or opposite of a, is a positive

number. Thus, is positive. For example, if then

if ais negative.

Finding Absolute Value

Simplify by finding each absolute value.

(a) (b)

(c) (d)

(e)

(f ) Work as in part (e);

(g) Evaluate each absolute value, and then add.

(h) -| 5 - 2 |=-| 3 |=- 3 Subtract inside the bars first.

|- 2 |+| 5 | = 2 + 5 = 7

- |- 8 |=- 182 =- 8 |- 8 |=8.

- | 8 |=- 182 =- 8

| 0 |= 0 |-0.75|=0.75

| 13 | = 13 |- 2 |=- 1 - 22 = 2

EXAMPLE 5

|a|= |- 3 |=- 1 - 32 = 3. |a|=-a

|a| a=-3,

- a,

|a|=-a

NOW TRY

Evaluate the absolute value.

Then find the additive inverse.

Comparing Rates of Change in Industries

The projected total rates of change in employment (in percent) in some of the fastest-

growing and in some of the most rapidly declining occupations from 2006 through

2016 are shown in the table.

EXAMPLE 6

Total Rate of Change

Occupation (2006–2016) (in percent)

Customer service representatives 24.8

Home health aides 48.7

Security guards 16.9

Word processors and typists

File clerks

Sewing machine operators -27.2

• 41.3


• 11.6

NOW TRY ANSWERS Source: Bureau of Labor Statistics.

5. (a) 7 (b)- 15 (c) 0