Let’s say a movie ticket costs less than \$10. If $c$ represents the cost of a movie ticket, we can use $c < 10$ to express what we know about the cost of a ticket.

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

For example, 5 is a solution to the inequality $c < 10$ because $5<10$ (or “5 is less than 10”) is a true statement, but 12 is not a solution because $12<10$ (“12 is less than 10”) 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 can describe the number of minutes that it rained ($r$) with the following inequalities and number lines. $$r > 10$$

$$r < 30$$

Any number of minutes greater than 10 is a solution to $r>10$, and any number less than 30 is a solution to $r<30$. 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.