Homework Help Compound Inequalities

A compound inequality contains at least two inequalities that are separated by either "and" or "or".

The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities. A number is a solution to the compound inequality if the number is a solution to both inequalities. It can either be written as x > -1 and x < 2 or as -1 < x < 2.

The graph of a compound inequality with an "or" represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities. It is written as x < -1 or x > 2


Video lesson

Solve and graph the linear inequality

$$-10 < 2 + x < -1$$

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So far, we've just been solving inequalities with two parts: a left side and a right side like this

But, sometimes we'll have inequalities with three parts:

Sometimes, these are called compound inequalities.

So, what do we do on these?

Our goal is the same:

On these, we just get him alone in the middle section.  So, just like before, pretend that there are really = signs and go about your business...  We'll just be working all three sections at once.

Let's go:

Get the x alone in the middle...


But, what does this mean?

x can be-1... or x can be3...or x can be a number between-1 and 3... like 0 or 2.315.

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