Question

How do you graph the inequality x < 1 on a coordinate plane?

Answer 1

Hint: The plot of an inequality is an area on a coordinate plane. First, plot the line for the equation $x=1$ and then shade the area for which the x coordinates of all the points in that area are less than 1.

Complete step by step answer:
Let us first understand what is meant by an inequality.
As the same suggests, inequality refers to something (say some variable) being not exactly equal to something. In other words, we can say that the value of the quantity is not exactly known but we do know some restriction or condition for the value of the quantity.
For example, suppose we have a stick in our hand and we want to measure the length of that stick. However, we do not have any measuring instrument to measure its length. Now, we approximate the length of the stick and we surely know that the stick cannot be more than one metre (by using some other stick whose length is exactly one metre).
Here, the length (L) of the stick is unknown but it is true that the length is less than one metre.
i.e. L < 1m
It is given that x < 1.
Now, if we plot the above inequality then we have to consider all the points on the coordinate plane where the x-coordinate is greater than one. It will be an area where all the points have x < 1.
We can shade that area by drawing the line $x=1$ as this line makes the boundary condition for the inequality.
We know that line $x=1$ is a vertical line passing through $x=1$. The area (region) to the right side of this has all the points with x < 1. Therefore, this area is the area where the inequality holds true.

Note: Note that the first step for plotting the region where the inequality holds true, is to write and the plot the equation by replacing the inequality by equal sign.
 If the plot is of a line, then the area above the line is for the inequality which has greater than sign and the area below the line is for lesser than sign.