An inequality that describes a real-world situation may have number solutions that make the inequality true, but those solutions may not always make sense in real life. 

For example:

• A basketball player scored more than 11 points in a game. This can be represented by the inequality , where is the number of points scored. Numbers such as 12, , and 130.25 are all solutions to the inequality because they each make the inequality true.

  In a basketball game, however, it is only possible to score a whole number of points, so fractional and decimal scores are not possible. It is also highly unlikely that one person would score more than 130 points in a single game.

  This particular situation limits the solutions.

Here is another example:

• It rained for less than 30 minutes yesterday (but it did rain). This can be represented by the inequality , where represents the number of minutes of rain yesterday. Even though numbers such as 18.2, and -7 are all less than 30, our solutions are limited to positive numbers since 0 or a negative number of minutes would not make sense in this context.

  To show the upper and lower boundaries, we can write two inequalities:

Inequalities can also represent a comparison of two unknown numbers.

• Let’s say we know that a puppy weighs more than a kitten, but we do not know the weight of either animal. We can write either of the following inequalities to represent this: or , where represents the weight of the puppy in pounds, and represents the weight of the kitten in pounds.