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Lesson 113: Graphing Inequalities
We've worked with inequalities like x > 4. In this short and easy lesson, we'll learn how to graph them.
Very often we are asked to represent inequalities graphically. We do this in a special way using a number line.
Take a look at the picture below:
This graph represents the inequality x > 1. We use an empty circle to mean that x cannot exactly equal 1, but any number greater is fine. That is what the heavy line with an arrow means. Don't get confused because the heavy arrow stops at 4. We had to stop it somewhere for visual purposes, but the arrow really means that it goes on forever. Any number greater than 1, such as 7, or even one million satisfies the inequality.
Let's look at another:
This is the graph of x ≤ 3. Remember that this symbol means "less than or equal to." We use a filled in circle to show that x can be exactly 3, and the arrow shows that it can be any value less than 3. Don't get tricked if the problem is presented to you as 3 ≥ x. It's the exact same thing, just written in reverse order, like we're reading from right to left.
Here is another:
This is the graph of -4 < x ≤ 3. This means that x must be between -4 and 3. It cannot equal 4, so we use an empty circle, but it can equal 3, so we use a filled in circle. The thick line shows us that all points in between satisfy the inequality.
You might run into some other types of inequalities, but if you understand everything shown in this lesson, you will not have any problem at all. Be sure to memorize the meaning of the empty and filled in circles.
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