Math Tip of the Week – Graphing Linear Inequalities

First of all, my heart goes out to the people of Moore, Oklahoma. I grew up in Tulsa, my daughter went to OU, and I’ve driven through Moore many times.

Let’s talk a little bit about solving and graphing Linear Inequalities. Here is an excerpt from the Linear Inequalities Section in Beginning Algebra:

When solving linear inequalities, you can solve as if you have an equality. You must have the variable on the left hand side when you use these rules to know where to graph:

  • When you have the less than sign (<), you want to graph to the left (both start with “le”); when you have the greater than sign (>) you graph to the right.
  • You can also graph in the direction where the inequality sign is pointed.
  • You can also plug in a number to see if it works: if it works, it should be on the colored part of the number line – like 3 is for the inequality “x < 4” (since 3 is less than 4).

Here are some examples, including the solutions in Interval Notation. Remember that with Interval Notation, you always go from lowest to highest number with “(“ (soft brackets) if the inequality doesn’t hit the point, and “[“ (hard brackets) if the inequality does hit the line. If you have to skip over any numbers, you do so by using the “U” sign, which means union, or put the things together.


Graphs Of Linear Equalities Table


Note that when you solve an inequality, you pretend like the inequality is an equal sign. The only thing you have to worry about is multiplying or dividing by a negative number; when you do this, you have to reverse the inequality symbol (change < to >, or > to <). You can see an example of this in the last equation below. The reason we need to do this, is when we have a negative coefficient(what comes before the variable), we’d eventually have to move the variable with its coefficient to the other side and make it positive, so it would be on the other end of the inequality sign.

At this point, we are not multiplying or dividing by variables (since we don’t know the signs of them); we will learn how to do that later.

Solving Inequalities

Hope this helps, and Happy Mathing!



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