Writing Inequality in Reverse Order

Inequality can be written in the reverse order. For example, if 2 is less than 5, then 5 must be greater than 2

i.e

\( \scriptsize 2 < 5 \: \rightarrow \: 5 > 2 \)

The inequality sign \( \scriptsize < \) has changed to \( \scriptsize > \)

Below are some more examples:

\( \scriptsize 5 < 10\) also means that \( \scriptsize 10 > 5 \)

\( \scriptsize r > 10\) also means that \( \scriptsize 10 < r \)

\( \scriptsize r \geq 10\) also means that \( \scriptsize 10 \leq r \)

Example 7.2.1:

Describe each of the following statements in words:

(a) \( \scriptsize 11 < 21\)

(b) \( \scriptsize 8 > 3\)

(c) \( \scriptsize -6 > \: -15 \)

(d) \( \scriptsize x < -5\)

(e) \( \scriptsize x \geq \: -14\)

(f) \( \scriptsize y \leq \: -5\)

Answers:

(a)  11 is less than 21 

(b)  8 is greater than 3 

(c)  -6 is greater than -15 

(d)  x is less than – 5 

(e)  x is greater than or equal to -14

(f) y is less than or equal to -5

Example 7.2.2:

Write the range of values of x in the following:

(a) \( \scriptsize x > 3 \)

(b) \( \scriptsize x \leq 5 \)

(c) \( \scriptsize x \geq 6 \)

(d) \( \scriptsize x > 6 \)

Answers

(a)  x = 4, 5, 6, 7, 8, …

(b)  x = 5, 4, 3, 2, 0, -1, -2, …

(c)  x = 6, 7, 8, 9, 10, … 

(d)  x = 7, 8, 9, 10, …

Example 7.2.3:

Rewrite these inequalities in reverse order:

(a) \( \scriptsize x > 3 \)

(b) \( \scriptsize 11 < 21\)

(c) \( \scriptsize 8 > 3 \)

(d) \( \scriptsize y \geq 6 \)

(e) \( \scriptsize z \leq \: -5 \)

Answers

(a) \( \scriptsize 3 < x \)

(b) \( \scriptsize 21 > 11\)

(c) \( \scriptsize 3 < 8 \)

(d) \( \scriptsize 6 \leq y \)

(e) \( \scriptsize -5 \geq \: z \)

Example 7.2.4:

For each of the following, choose a letter and write an inequality: 

(a) The price of a house is over  ₦5000
(b) The man’s height is 1.6 m or less 
(c) An acute angle is less than 90º

Solution 

(a) Let the price of the house be x

x is over ₦5000 means x \( \scriptsize > \) ₦5000

(b) Let the man’s height be y 

⇒ \( \scriptsize y \leq 1.6\:m \)

(c) Let the acute angle be a 

\( \scriptsize a < 90^{\circ} \)

Evaluation Questions: