### Theory:

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 $3x+9\le 18$ in a number line, where $$x$$ is an integer.

The given expression is $3x+9\le 18$.

Now solve it using the inequation rules.

Step - $$1$$: Subtract both sides by $$-9$$.

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

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

$\begin{array}{l}\frac{3x}{3}\le 9\\ \\ x\phantom{\rule{0.147em}{0ex}}\le 3\end{array}$

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