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Lesson 6, Topic 3
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# Graphs of Linear Inequalities

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Inequalities are said to be linear, if they have no square or higher powers of the unknown. In other words, the highest power of the unknown is 1.

E.g

$$\scriptsize 2x > 10$$

$$\scriptsize 4x \: – \: 5y > \: -18$$

### Number Line

A number line is a visual representation of the set of real numbers as a series of points.

### Showing Inequalities on a Number Line

On a number line, you can show inequality by obeying these rules.

For ‘<’ the arrow points to the left, but the starting point is not shaded

For Example, x < 5 is drawn this way

For ‘>’, the arrow points to the right direction and the starting point is not shaded.

E.g. x > 5 is drawn this way

3. For $$\scriptsize ‘ \leq ‘$$ , the arrow points to the left and the starting point is shaded.

e.g $$\scriptsize x \leq \: -2$$, is drawn this way.

3. For $$\scriptsize ‘ \geq ‘$$ , the arrow points to the left and the starting point is shaded.

e.g $$\scriptsize x \geq \: -2$$, is drawn this way.

### Example 1

Show the following inequalities on a number line

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

(b) $$\scriptsize x \leq 3$$

(c) $$\scriptsize x \geq 3$$

Solution

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

(b) $$\scriptsize x \leq 3$$

(c) $$\scriptsize x \geq 3$$

### Example 2

Show each of these inequalities on a number line

(a) $$\scriptsize x < 4$$

(b) $$\scriptsize x > 4$$

(c) $$\scriptsize x \leq 4$$

(d) $$\scriptsize x \geq 4$$

Solution

(a) $$\scriptsize x < 4$$

(b) $$\scriptsize x > 4$$

(c) $$\scriptsize x \leq 4$$

(d) $$\scriptsize x \geq 4$$

### Example 3

Use suitable symbols to write the inequalities shown in the following number line

(a)

(b)

(c)

(d)

(a) $$\scriptsize x \geq -3$$
(b) $$\scriptsize x \leq 2$$
(c) $$\scriptsize x \geq -1$$
(d) $$\scriptsize x < 5$$ 