Question

In a compound inequality when do you use the (And) and when do you use the (Or) in a statement

Answer 1

In a compound inequality, you use the and when the solutions for x along the number line overlap. For example, suppose you have

x > 3 and x < 10

Then you can re-write this as

3 < x < 10

which is an equivalent expression that simply means the range of solution values for the compound inequality are between 3 and 10.

Answer 2

Now suppose you have

x < 3 or x > 5

This means that the solutions do not overlap and you cannot combine it into an expression of the form a < x < b because the range of solution values do not overlap. Instead, the range of solutions for one equality goes toward positive infinity, while the other goes towards negative infinity.

Answer 3

And in (OR)