We use a number line to compare numbers. On a number line, all the numbers to the right of a number are greater than that number. All the numbers to the left of a number are smaller than that number.

Look at the numbers on Figure 2.11. All the numbers to right of –3 are greater than –3. That is, [–2, –1, 0, 1, 2, 3, 4, 5, 6, …] are greater than –3. Or, all the numbers [ –4, –5, –6, …] are smaller than -3.

Figure 2.11

We usually use the signs in Table 2.12 to compare all numbers.

Table 2.12

Notice that the small end of the inequality sign points to the smaller number. When dealing with inequalities, it is wise to remember that if 7 is less than 12 (7 < 12), then 12 is greater than 7 (12 > 7).

Practice 9. Place < or > between each pair of numbers.
 
(a) –4 ___ 12
 
(b) 23 ___ –21
 
(c) –145 ___ –211
 
(d) 29 ___ –32
 
(e) –101 ___ –110
 
Answers
 
 
Practice 10. Order the numbers below using inequality signs.
 
21, –11, 0, 43, 11, –19, 54, –45, –25, 19
 
Answer
 
 
Practice 11. Which integers in Figure 2.13 are smaller than 6 and greater than –3?

Figure 2.13

Answer
 
 
Practice 12. Which statements are true?
 
(a) –3 < 5 < 6
 
(b) 4 > 7 > –8
 
(c) 11 < 12 < –13
 
(d) –12 < 12 < 13
 
(e) 24 < 0 < –24

(f) –53 < 0 < 35
 
(g) 49 > 0 > –99

Answers
 
 
Real Life Application 5. Andy has $25. Beth has $15. Carol has $20. We’ll call the amount of money Andy has A, the amount of money Beth has B and the amount of money Carol has C. Which of these is statements is true or false?

1. A > B + C
    
2. B < A + C
    
3. C > B + A
    
4. B < A – C
    
5. A > B – C
    
6. B < A
    
7. B + C > A
    
8. A + B + C > $35
    
9. C > B

Answers
 
 
Practice 13. Simplify each statement. Then determine whether it is true or false.
 
(a) –4 + 5 > 23 – 11 + 3
 
(b) 12 – 32 < 11 + 3
 
(c) –7 – 11 ≤ 212 + 11 – 3
 
(d) 6 – 15 ≥ –15 + 6


Answers
 
 
Practical Exercise 2. Which statements are true, if m > –1 is a false statement?
 
m = –1, m = –2, m = 10, m = 1, m = 2
 

Answers