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Lesson 6, Topic 1
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# Linear Inequalities – Introduction

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### Meaning of Inequality

An inequality is a sentence that says that two values are not equal. E.g. if a is not equal to b, we can write a ≠ b (where ≠ means “is not equal to”). Therefore, inequalities are used to compare the relative sizes of values like integers, variable, etc.

### Inequality Symbols

The following are inequality symbols

### $$\scriptsize {\color{Yellow} > }$$ (“is greater than”)

e.g

$$\scriptsize 5 > 3$$ means 5 “is greater than” 3

$$\scriptsize y > 10$$ the values of y include 11, 12, 13, 14 ……

### $$\scriptsize {\color{Yellow} < }$$ (“is less than”)

e.g

$$\scriptsize 3 < 5$$ reads 3 “is less than” 5

$$\scriptsize y < 10$$ the values of y include 9, 8, 7, 6 ……

### $$\scriptsize {\color{Yellow} = }$$ (“is equal to”)

e.g.

$$\scriptsize 2 \: + \: 3 = 5$$

### $$\scriptsize {\color{Yellow} \geq }$$ (“is greater than or equal to”)

e.g

If $$y \scriptsize \geq 10$$ the values of y include: 10, 11, 12, 13, … (i.e. the value 10 is included).

### $$\scriptsize {\color{Yellow} \leq }$$ (“is less than or equal to”)

e.g

If $$y \scriptsize \leq 10$$ the values of y include: 10, 9, 8, 7,6, … (the value 10 is included).

Note:

y ≥ 10 means values of y that are equal to 10 or greater than 10.

### Example 1

Write the following inequalities in statement and list the range of values.

(a) $$\scriptsize x < 2$$

(b) $$\scriptsize x > 2$$

(c) $$\scriptsize x \leq 2$$

(d) $$\scriptsize x \geq 2$$

Solution

(a) $$\scriptsize x < 2$$ reads x is less than 2

Range of values x = 1, 0, -1, -2, -3, -4, …

(b) $$\scriptsize x > 2$$reads x is greater than 2

Range of values of x = 3, 4, 5, 6, 7, 8, …

(c) $$\scriptsize x \leq 2$$ reads x is less than or equal to 2

Range of values of x = 2, 1, 0, -1, -2, -3, -4, …

(d) $$\scriptsize x \geq 2$$reads x is greater than or equal to 2

Range of values of x = 2, 3, 4, 5, 6, 7, 8, 9, 10, …

error: