We can write inequalities to represent situations and solve problems. First, it’s important to decide what quantity we are representing with a variable. Next, we can connect the quantities in the situation to write an expression. Then we choose an inequality symbol and complete the inequality.

When solving the inequality to answer a question about the situation, it’s important to keep the meaning of each quantity in mind. This helps us decide if the solution to the inequality makes sense for the situation.

Example: Han has 50 centimeters of wire and wants to make a square picture frame with a loop to hang it. He uses 3 centimeters for the loop. If Han wants to use all the wire, this situation can be represented by the equation $3+4s=50$, where $s$ is the length of each side in centimeters.

If Han doesn’t need to use all the wire, we can represent the situation with the inequality $3+4s\leq50$. The solution to this inequality is $s \leq 11.75$. However, not all solutions to this inequality make sense for the situation. For example, we cannot have negative lengths or a side length of 0 centimeters.

In other situations, the variable may represent a quantity that increases by whole numbers, such as numbers of magazines, loads of laundry, or students. In those cases, only whole-number solutions make sense.