Beginning Algebra, 11th Edition

Finding the Absolute Value

Simplify by finding the absolute value.

(a) (b) (c)

(d) (e)

(f ) (g)

Parts (f ) and (g) show that absolute value bars are grouping symbols. We perform

any operations inside absolute value symbols beforefinding the absolute value.

NOW TRY

OBJECTIVE 5 Interpret the meanings of real numbers from a table of

data.

| 8 - 2 |=| 6 | = 6 - | 8 - 2 |=-| 6 | =- 6

- | 5 |= - 152 =- 5 - |- 5 | = - 152 =- 5

| 0 |= 0 | 5 |= 5 |- 5 |=- 1 - 52 = 5

EXAMPLE 4

SECTION 1.4 Real Numbers and the Number Line 33

CAUTION The “ ” in the second part of the definition of absolute value does

NOTrepresent a negative number. Since xis negative in the second part, repre-

sents the opposite of a negative number—that is, a positive number. The absolute

value of a number is never negative.

- x

- x

NOW TRY
EXERCISE 4
Simplify by finding the
absolute value.

(a)| 4 | (b)|- 4 | (c) -|- 4 |

NOW TRY ANSWERS

4. (a) 4 (b) 4 (c)


5. new cars
   
   
   • 4
   
   
   
   

NOW TRY
EXERCISE 5
In the table for Example 5,
which category represents a
decrease for both years?

Change from Change from

Category 2005 to 2006 2006 to 2007

Education 6.2 5.7

Food 3.2 2.8

Gasoline 12.9 8.2

Medical care 4.0 4.4

New cars 0.2 1.0

Source:U.S. Bureau of Labor Statistics.

(a)What category in which year represents the greatest percent decrease?

We must find the negative number with the greatest absolute value. The number

that satisfies this condition is so the greatest percent decrease was shown by

new cars from 2006 to 2007.

(b)Which category in which year represents the least change?

We must find the number (either positive, negative, or zero) with the least absolute

value. From 2005 to 2006, new cars showed the least change, a decrease of 0.2%.

NOW TRY

- 1.0,

Interpreting Data

The Consumer Price Index (CPI) measures the average change in prices of goods and

services purchased by urban consumers in the United States.

The table shows the percent change in the Consumer Price Index for selected cat-

egories of goods and services from 2005 to 2006 and from 2006 to 2007. Use the

table to answer each question.

EXAMPLE 5