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.
 
img1.png
 
ii) When \(x ≥ 4\), the solutions of \(x\) are \(4\), \(5\), \(6\), \(7\), \(8\)…… And its graph on the number as shown below.
 
img2.png
 
iii) Similarly, if \(x < 2\), the solutions of \(x\) are \(1\), \(0\), \(-1\), \(-2\), \(-3\)…… And its graph on the number as shown below.
 
img3.png
Example:
Represent the solutions of 3x+918 in a number line, where \(x\) is an integer.
 
The given expression is 3x+918.
 
Now solve it using the inequation rules.
 
Step - \(1\): Subtract both sides by \(-9\).
 
3x+991893x+01893x9
 
Step - \(2\): Divide by 3 on both sides.
 
3x39x3
 
Since the solution belongs to integers, the solutions are 3, 2, 1, 0, −1, …. Its graph on the number line is shown below:
 
img4.png