Graphing inequalities on a number line

Graphing inequalities on a number line is used to find visual solutions of inequalities. There are few processes which can make the students learn pretty easily how this can be done.

We will discuss about the method of graphing inequalities on a number line. There are some instructions which are given in this article for understanding the method more easily. Drawing the number line is the first thing to be done. Firstly, the student needs to draw a straight horizontal line. Then arrows must be given to the both ends of the straight line. We cannot increase the line to infinity. So the arrows are given as if on the line infinite numbers can be placed. Then on the straight horizontal line small vertical lines must be drawn. These small vertical lines must be drawn in a way such that the distance between two lines can always be same. The interval depends on how many numbers are graphed.

Then below the vertical lines numbers must be placed in a way that it can look like the picture.

To find the inequality solution first the student needs to know what the inequality solution requires. This means the equation showing any unknown object like x or y greater than or less than any number. A solid dot must be drawn on the number which is greater or less than the unknown value (i.e. x or y or anything like a, b, c, d etc) on the horizontal straight line. Then an arrow must be drawn to show the direction of the inequality toward infinity. The arrow must be bold to show direction of the inequality. This arrow represents the numbers which fulfill the inequalities. From the next image the student can understand it more clearly.

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The earlier description is for greater than inequality. Now we assume that x is less than 1. Then a dot must be given on the starting point of the inequality. This point is not in the inequality equation though. But this point is the point from where the inequality starts. Similar to the earlier process an arrow must be drawn to show the direction of the inequality to infinity. From the dot, a thick line must be drawn to distinguish the direction from the horizontal straight line to the point of the arrow. This arrow represents all the numbers satisfying the inequality. So the figure will look like-

This is the method of graphing inequality on a number line. Doing sums may help the student to understand the method better.