What should I do if my teacher wants me to solve an inequality on a number line?

The solutions to inequalities can be expressed in several ways. You can use inequality notation, interval notation, or a shaded number line. Each of these ways of describing a solution has its place in different application. None is better than another. They're just different and used for different purposes.
The number line is very helpful when solving multiple inequalities. It's an essential part of solving absolute value inequalities. Two key words in the solutions of these problems are and and or. In mathematics, these two words have very specific meanings. The word and means that both requirements must be met. The word or means that one requirement or the other or both must be met.