What is an Inequality?

An introduction to what an inequality is and why we need them.

 

Let’s continue this idea by looking at the finer details of graphing inequalities.

Graph:     $ \color{blue}{x < 4}$

Lets start by graphing some of the numbers that make the statement $x < 4$ true.

graphing points less than four

These are only a few of the solutions. We use need to use a line to show that all the numbers less than 4 are included. Also by putting an open circle where the start of the solution is (around the 4) we are saying that while $3.99999$ is part of the solution set, 4 is not.

graphing the inequality x is less than 4

When the the number is not included in the solution set the circle is open.

 

Graph:     $ \color{blue}{x \leq 4}$

Again we will use a line to show that all the numbers less than 4 are included, but this time we put a closed circle (which means that we color in the circle) around the number where the start of the solution is. So in this case, the filled in circle around the 4 is telling the reader that 4 is part of the solution set.

graphing the inequality x is less than or equal to four

When the the number is included in the solution set the circle is filled in.

 

Graph:     $ \color{blue}{x > 4}$

Pick a value for x to determine which way to draw the line representing the solution set. Since 6 is greater than 4 the line is drawn to the right.
Graphing the inequality x is greater than four

When the the number is not included in the solution set the circle is open.