A compound inequality is a statement in which two inequalities are connected by the word "and" or the word "or".

For example, x > 5 and x ≤ 7 and x ≤ -1 or x > 7 are examples of compound inequalities

When the word that connects both inequalities is "and", the solution is any number that makes both inequalities true

When the word that connects both inequalities is "or", the solution is any number that makes either inequalities true

For example, graph the following compound inequality: x ≥ 2 and x < 4

The graphs for x ≥ 2 and x < 4 should look like this:

If you pull this out from the graph above, we get:

Notice that the open circle (in red) means that 4 is not included

Graph x ≥ - 2 and x > 1

The graphs for x ≥ - 2 and x > 1 should look like this:

If you pull this out from the graph above, we get:

However, if we twist the same problem above and graph x ≥ - 2 or x >, it is a different story

Since the "or" means either, the solution will be the shaded area that include both inequalities.

The solution is thus any number after -2

Graph x > 2 or x < -3

Here it is!

Look carefully again at the graph right above and you will see that blue and red don't meet. That is why they have nothing in common and thus no solutions