We can write and solve inequalities to solve problems.

Example:  Elena has $5 and sells pens for $1.50 each. Her goal is to save $20. We could solve the equation LATEX0 to find the number of pens, LATEX1, that Elena needs to sell in order to save exactly $20. Adding $-5$ to both sides of the equation gives us $1.5x=15$, and then dividing both sides by 1.5 gives the solution $x=10$ pens.

What if Elena wants to save more than $20? The inequality LATEX5 tells us that the amount of money Elena saves needs to be greater than $20. The solution to the previous equation will help us understand what the solutions to the inequality will be. We know that if Elena sells 10 pens, she will save exactly $20. Since each pen gives her more money, she needs to sell more than 10 pens to save more than $20. So, we can represent all the solutions to the inequality with another inequality: $x>10$.  A solution to an inequality is a number that can be used in place of the variable to make the inequality true.