Introduction to Integers
Read this text, which explains the concept of negative numbers using number lines. Pay close attention to the section "Opposite Notation", as this notation will come up frequently in the next few sections of this course. Complete the practice questions and check your answers.
Examples
Solutions
Example 3.1
Solution
Draw a number line. Mark 0 in the center and label several units to the left and right.
ⓐ To plot 3, start at 0 and count three units to the right. Place a point as shown in Figure 3.7.
Figure 3.7
ⓑ To plot −3, start at 0 and count three units to the left. Place a point as shown in Figure 3.8.
Figure 3.8
ⓒ To plot −2, start at 0 and count two units to the left. Place a point as shown in Figure 3.9.
Figure 3.9
Example 3.2
Solution
Begin by plotting the numbers on a number line as shown in Figure 3.12.
Figure 3.12
ⓐ Compare 14 and 6. 14___6
14 is to the right of 6 on the number line. 
ⓑ Compare −1 and 9. −1___9
−1 is to the left of 9 on the number line. 
ⓒ Compare −1 and −4. −1___−4
−1 is to the right of −4 on the number line. 
ⓓ Compare 2 and −20. −2___−20
2 is to the right of −20 on the number line. 
Example 3.3
Solution
ⓐ The number −7 is the same distance from 0 as 7, but on the opposite side of 0. So −7 is the opposite of 7 as shown in Figure 3.14.
Figure 3.14
ⓑ The number 10 is the same distance from 0 as −10, but on the opposite side of 0. So 10 is the opposite of −10 as shown in Figure 3.15.
Figure 3.15
Example 3.4
The opposite of −6 is 6.
Example 3.5
Solution
ⓐ To evaluate  when  , substitute 8 for  . |
|
|---|---|
| Substitute 8 for |
 |
| Simplify. | −8 |
ⓑ To evaluate when  , substitute −8 for . |
|
|---|---|
| Substitute −8 for |
 |
| Simplify. | 8 |