Many real-world problems can be represented and solved by using inequalities. Writing inequalities is very similar to writing equations to represent a situation. The expressions that make up the inequalities can be thought of in much the same way as the expressions that make up equations. For inequalities, we also have to think about how expressions compare to each other—which one has a greater value, which one has a lesser value, and can they also be equal?

For example, a school fundraiser has a minimum target of $500. Faculty have donated $100 and there are 12 student clubs that are participating with different activities. How much money would each club need to raise if the 12 clubs shared the responsibility of meeting the goal equally? If $n$ is the amount of money that each club raises, then the solution to $100+12n=500$ is the amount each club has to raise to meet the goal. It is more realistic, though, to use the inequality $100+12n\geq500$, since the more money raised, the more successful the fundraiser. There are many solutions because there are many different amounts of money the clubs could raise that would get them above their minimum goal of $500.