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Lesson 6, Topic 2
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# Writing Inequality in Reverse Order

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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 $$\scriptsize >$$

### Example 1

$$\scriptsize 5 < 10$$ also means that $$\scriptsize 10 > 5$$

$$\scriptsize r > 10$$ also means that $$\scriptsize 10 < r$$

$$\scriptsize r \geq 10$$ also means that $$\scriptsize 10 \leq r$$

### 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) $$\scriptsize y \leq \: -5$$

(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

### 2. Write the range of values of x in the following

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

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

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

(e) $$\scriptsize x > 6$$

(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, …

### 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) $$\scriptsize z \leq \: -5$$

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

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

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

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

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

### Example 3

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

(a) The price of a house is over  N5000

(b) The man’s height is 1.6m or less

(c) An acute angle is less than 90º

Solution

(a) Let the price of the house be x

x is over N5000 means x $$\scriptsize >$$ N5000

(b) Let the man’s height be y

:- $$\scriptsize y \leq 1.6m$$

(c) Let the acute angle be a

$$\scriptsize a < 90^o$$

Evaluation

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

1. Tolu’s age is over 10 years
2. My father has less than 50 goats
3. His cousin has nothing less than 50 goats
4. The cost of the building is over N200000
5. In 5 years’ time, the man’s age will still be under 50 years.

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