Let’s say a movie ticket costs less than $15. If represents the cost of a movie ticket, we can use  to express what we know about the cost of a ticket.

Any value of that makes the inequality true is called a solution to the inequality.

For example, 5 is a solution to the inequality  because  (or “5 is less than 15”) is a true statement, but 17 is not a solution because (“17 is less than 15”) is not a true statement.

If a situation involves more than one boundary, or limit, we will need more than one inequality to express it.

For example, if we knew that it rained for more than 10 minutes but less than 30 minutes, we could describe the number of minutes that it rained () with the following inequalities and number lines:

Any number of minutes greater than 10 is a solution to , and any number less than 30 is a solution to . But to meet the condition of “more than 10 but less than 30,” the solutions are limited to the numbers between 10 and 30 minutes, not including 10 and 30.

We can show the solutions visually by graphing the two inequalities on one number line.