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Home » Inequalities » Solving Compound Inequalities

In our last lesson, we solved compound inequalities that involved the word "and". These are called conjunctions.

In this lesson, we are going to solve the other type of compound inequality that is called a disjunction. These are the compound inequalities that contains the word "or".

There is really only one method to solving disjunction compound inequalities because you must solve each inequality separately.

Let's take a look at an example together.

Let's take a look at one more example. Remember the rule: *If you multiply or divide by a negative number, then you must reverse the inequality sign?* Well, that rule still applies. Take a look..

Again, we must solve each inequality separately and then graph the solutions on the same number line.

That's our final lesson on compound inequalities. Hopefully you can now tell the difference between a conjunction (using the word "and") and a disjunction (using the word "or"). Check out our other inequality lessons below for a thorough study of inequalities.

In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not.

The notation a b means that a is greater than b.

The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a 2 +750x-9000

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This chapter explores linear inequalities. Before attempting this chapter you must have prior knowledge of solving linear equations. The chapter covers solving linear inequalities, displaying the solutions on a number line, solving double-ended inequalities, and look at the intersection of two solutions.

Explanation: You must already know how to solve linear equations for example below is an equation to solve naturally.

First we expand the equation as shown below.

Arrange x terms on one side as shown below.

Now we can simplify as shown below

We divide both sides by 7 and the result becomes.

24 - x ≤ 3(2x + 1)

Explanation: We can use the same principle used above to solve the following inequality.

24 - x ≤ 3(2x + 1)

First we expand as shown below.

then divide both sides by 7 to simplify again. We get that;

Example: You may have a negative number of xs. For example below is an inequality that we could solve.