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3. Graphical representation of inequation

The solutions of inequations can be represented on a number line by marking the true values of the solutions with different colours.

Let us see how the various solutions of the

$x$ can be represented graphically on the number line.

Here, we consider the solutions belong to natural numbers. That is, every value of the solution is a natural number.

The coloured points on the number line shows the solutions of

$x$ .

i) When

$x ≤ 4$ , the solutions of

$x$ are

$4$ ,

$3$ ,

$2$ ,

$1$ ,

$0$ …... And its graph on the number as shown below.

ii) When

$x ≥ 4$ , the solutions of

$x$ are

$4$ ,

$5$ ,

$6$ ,

$7$ ,

$8$ …… And its graph on the number as shown below.

iii) Similarly, if

$x < 2$ , the solutions of

$x$ are

$1$ ,

$0$ ,

$-1$ ,

$-2$ ,

$-3$ …… And its graph on the number as shown below.

Example:

Represent the solutions of

$3 x + 9 \leq 18$ in a number line, where

$x$ is an integer.

The given expression is

$3 x + 9 \leq 18$ .

Now solve it using the inequation rules.

Step - $1$ : Subtract both sides by

$-9$ .

$\begin{array}{l} 3 x + 9 - 9 \leq 18 - 9 \\ 3 x + 0 \leq 18 - 9 \\ 3 x \leq 9 \end{array}$

Step - $2$ : Divide by 3 on both sides.

$\begin{array}{l} \frac{3 x}{3} \leq 9 \\ x \leq 3 \end{array}$

Since the solution belongs to integers, the solutions are 3, 2, 1, 0, −1, …. Its graph on the number line is shown below:

$1$

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