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» » Graphing Inequalities

Graphing Inequalities

Graphing inequalities is very similar to graphing linear equations. Once your linear equation is graphed, you then must focus on the inequality symbol and perform two more steps. It's pretty easy and fun. Stick with me and you'll have no problems by the end of this lesson.




This is a graph for a linear inequality. Notice how we have a boundary line (that can be solid or dotted) and we have a half plane shaded. (Hint: These are the two extra steps that you must take when graphing inequalities.)

graphing inequalities example

In order to succeed with this lesson, you will need to remember how to graph equations using slope intercept form.

There will be two additional steps that you must take when graphing linear inequalities.

As shown in this image, the first step will be to determine whether you will use a solid boundary line or a dashed boundary line. The inequality symbol will help you to determine the boundary line.

If the inequality symbol is greater than or less than, then you will use a dotted boundary line. This means that the solutions are NOT included on the boundary line.

If the inequality symbol is greater than or equal to or less than or equal to, then you will use a solid line to indicate that the solutions are included on the boundary line.

The second step will be to determine which half plane to shade.

If this all sounds confusing, don't worry.... Take a look at the examples below and it will all make sense.

So... first let's take a look at our graphing symbols. You may want to keep this handy for a reference.


graphing inequalities symbols



Our first example will demonstrate how to draw your boundary line and how to choose a test point in order to shade your graph. These are the two additional steps that we take when graphing inequalities. Take a look.....


Example 1


graphing inequalities

algebra inequalities




Did you notice how our boundary line was a dotted line because of the less than symbol that was used in the inequality?

Also, you may have realized that you shade below the dotted line because of the less than symbol in the inequality. However, if you are unsure you can always choose a test point. I always use the point (0,0) if it's not on the line.

Substitute (0,0) into the original inequality. If the math sentence is true once you substitute (0,0), then that means that (0,0) is a solution and you shade the half plane that contains (0,0). If the math sentence is false when you substitute (0,0), then that means that (0,0) is not a solution and the other half plane (or the side of the line that does not contain (0,0) should be shaded.



For this second example, we'll need to rewrite the equation so that it's in slope intercept form before we graph. Also take note that the sign is greater than or equal to, so we will graph a solid line this time instead of a dotted line. This example will also demonstrate how to choose three solutions to the inequality.



Example 2


graphing inequalities examples

inequality examples





Our last example reinforces how you must REVERSE THE SIGN if you MULTIPLY or DIVIDE by a negative number! Let's take a look.




Example 3


algebra inequality problems
algebra inequality examples




Want to try a few on your own? Try these practice problems.



Are You Still Having Trouble Graphing Linear Inequalities?

Enter your inequality and click "Draw".





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