Are you still looking for a simple procedure on how to represent the solution set of an inequation on a graph? If yes, then stay on this page. Here we are giving a detailed step by step explanation on finding Solution Set for **Linear Inequations** with the solved examples. So, refer to the following sections and solve the questions easily.

## Graphical Representation of the Solution Set of an Inequation

We generally use a number line to represent the solution set of an inequation on a graph. Following are the steps to represent the solution set of a linear inequation on a graph.

- At first, solve the given linear inequation and find the solution set for it.
- Mark the solution set on a number line by putting dot.
- If the solution set is infinite, then put three more dots to indicate infiniteness.

### Questions on Finding the Solution Set of an Inequation and their Representation

**Example 1.**

Solve the inequation 4x – 6 < 10, x ∈ N and represent the solution set graphically?

**Solution:**

Given linear inequation is 4x – 6 < 10

Add 6 to the both sides of inequation

= 4x – 6 + 6 < 10 + 6

= 4x < 16

Divide both sides of the inequation by 4

= 4x/4 < 16/4

= x < 4

So, the replacement set = {1, 2, 3, 4, . . }

Therefore, the solution set S = {1, 2, 3} or S = {x : x ∈ N, x < 4}

Let us mark the solution set graphically.

The solution set is marked on the number line by dots.

**Example 2.**

Solve the inequation 8x + 4 > 20, x ∈ W and represent the solution set graphically?

**Solution:**

Given linear inequation is 8x + 4 > 20

Subtract 4 from both sides

= 8x + 4 – 4 > 20 – 4

= 8x > 16

Divide both sides by 8

= 8x/8 > 16/8

= x > 2

Replacement set = {0, 1, 2, 3, 4, . . . }

Therefore, solution set = {3, 4, 5, . . } or S = {x : x ∈ W, x > 2}

Let us mark the solution set graphically.

The solution set is marked on the number line by dots. We put three more dots indicate the infiniteness of the solution set.

**Example 3.**

Solve -2 ≥ x ≥ 5, x ∈ I, and represent the solution set graphically?

**Solution:**

Given linear inequation is -2 ≥ x ≥ 5

This has two inequations,

-2 ≥ x and x ≥ 5

Replacement set = {. . . -3, -2, -1, 0, 1, 2, 3 . . .}

Solution set for the inequation -2 ≥ x is -2, -1, 0, 1, 2, 3, . . i.e S = {-2, -1, 0, 1, 2, 3 . . } = P

And the solution set for the inequation x ≥ 5 is 5, 6, 7, 8 . . i.e Q = {5, 6, 7, 8 . . .}

Therefore, solution set for the given inequation = P ∩ Q

= {5, 6, 7, 8, 9 . . . }

or S = {x : x ∈ I, -2 ≥ x ≥ 5}

Let us represent the solution set graphically.

The solution set is marked on the number line by dots.

**Example 4.**

Solve 0 < 3x – 10 ≤ 12, x ∈ R and represent the solution set graphically.

**Solution:**

Given linear inequation is 0 < 3x – 10 ≤ 12

It has two cases.

Case I:

0 < 3x – 10

Add 10 to both sides

0 + 10 < 3x – 10 + 10

10 < 3x

Divide both sides by 3

10/3 < 3x/3

10/3 < x

Case II:

3x – 10 ≤ 12

Add 10 to both sides

3x – 10 + 10 ≤ 12 + 10

3x ≤ 22

Divide both sides by 3

3x/x ≤ 22/3

x ≤ 22/3

S ∩ S’ = {3.33 < x ≤ 7.33} x ∈ R

= {x : x ∈ R 3.33 < x ≤ 7.33}