Basic Mathematics for College Students

The absolute valueof a number gives the distance between the number and 0 on

the number line. To indicate absolute value, the number is inserted between two

vertical bars, called the absolute value symbol.For example, we can write.

This is read as “The absolute value of negative 3 is 3,” and it tells us that the distance

between and 0 on the number line is 3 units. From the figure, we also see that

030  3.

 3

0  30  3

There are three other commonly used inequality symbols.

136 Chapter 2 The Integers

The Language of Mathematics Because the symbol requires one number

to be strictly less than another number and the symbol requires one number

to be strictly greater than another number, mathematical statements involving

the symbols and are called   strict inequalities.





EXAMPLE (^3) Tell whether each statement is true or false.
a. b. c. d.
StrategyWe will determine if either the strict inequality or the equality that the
symbols and allow is true.
WHYIf either is true, then the given statement is true.
Solution
a. This statement is true, because  9 9.
b. This statement is false, because neither  1 5 nor  1 5 is true.
c. This statement is false, because neither  27 6 nor  27 6 is true.
d. 32  31 This statement is true, because  32 31.

 27  6

 1  5

 9  9

 

 9  9  1  5  27  6  32  32

Self Check 3

Tell whether each statement is

true or false.

a.

b.

c.

d.

Now TryProblems 41 and 45

 61  62

 2  2

 35  35

 17  15

4 Find the absolute value of an integer.

Using a number line, we can see that the numbers 3 and are both a distance of 3

units away from 0, as shown below.

 3

− 5 − 4 − 3 − 2 −101 23 4 5

3 units 3 units

Inequality Symbols

means is not equal to

means is greater than or equal to

 means is less than or equal to



Read as “5 is not equal to 2.”

Read as “6 is less than or equal to 10.”

This statement is true, because  6 10.

Read as “12 is less than or equal to 12.”

This statement is true, because 12 12.

Read as “15 is greater than or equal to 17.”

This statement is true, because  15 17.

Read as “20 is greater than or equal to 20.”

This statement is true, because  20 20.

 20  20

 15  17

12  12

 6  10

 5  2