How to graph inequalities on number lines

One can undoubtedly say that Maths is all about playing with numbers. In this section, we will focus on a very important topic of Mathematics which is regarding the number lines. A horizontal line with points corresponding to numbers can be termed as a number line. The value of the numbers which the points correspond to in a number line help in understanding how the points are spread out. When a number line has mainly integers or whole numbers then the points are equally spread out. 

Use of Number Lines for Solving Inequalities

Firstly, for solving an inequality by the means of the number line, one first needs to change the sign of inequality into equality, and then one can begin solving the problem. The next step can be regarding graphing the point on that number line. One can divide the number line into separate regions. One region can be to the right of the point and another can be to the left of the point. Then all that one has to do is select a point from both the regions for testing it. The test can help in understanding if it contains the inequality when plugged in for the variable. Lastly, what one may do is if it is satisfactory for the inequality then a dark line can be drawn from the point to that particular region along with an end with the arrow. Thus, it can be concluded as the answer for the equation. One can infer that if a single point in the region is satisfying the inequality then the whole region shall be content for the inequality. 

• For example, for plotting the 3.5 on the number line, we first make a number line like this,

🡨—-[————————–]———–🡪

        -4  -3  -2  -1  0  1  2  3  4 

Now, for showing the inequality one can graph the number line such as 

🡨—]-(———————————-🡪 

 1 2 3 4 5 6

Thus, the space in between helps to understand the graphical representation of the inequality X < 3.5

• Further, for plotting 2.5 on the number line, we first make a number line like this.

🡨—-[————————–]———–🡪

        -4  -3  -2  -1  0  1  2  3  4 

Now, for showing the inequality one can graph the number line such as 

🡨–]-(———————————-🡪 

 0 1 2 3 4 5 6

Thus, the space in between helps to understand the graphical representation of the inequality X < 2.5

• Now, for showing the inequality one can graph the number line such as 

🡨—-[————————–]———–🡪

        -4  -3  -2  -1  0  1  2  3  4 

For understanding where the number -1.5 shall come from, 

🡨–]-(———————————-🡪 

 -2 -1 0 1 2 

Thus, the space in between helps to understand the graphical representation of the inequality X >-1.5

Thus, the above examples help gain an insight into the process of representing number lines and plotting points on the same. 

Conclusion

Thus, as observed from the above discussion Maths is a very insightful subject with several interesting topics, and today, we learned about one such significant topic which is regarding the number lines. From learning what is a number line to how one can plot it, various topics have been covered comprehensively. Further, we also focused on how to use number lines for finding the solution for the inequalities in a step-by-step manner. Thus, it can be concluded that various aspects of number lines have been discussed in this section in an easy-to-understand manner.