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# Equations and Inequalities

# Fitting Things in Spaces

If you aren't the greatest at maximizing closet space, you may have some direct experience being frustrated by this one. It will often come in handy to know how much room you are working with, and how much of a certain object or material can possibly go there.

### Sample Problem

Shin is building a shelf to put over his desk and hold his books. Each book is of an inch thick. Okay, they're issues of *Vogue*, but same difference. The board Shin is using is 2 ft long. How many "books" can Shin fit on the shelf?

This problem can be turned into an inequality. We're turning it into an inequality rather than an equation, because we might have a little space left over on the shelf. Let *x* be the number of "books" on the shelf. We'll stop putting quotes around "books" now, since it's exhausting. Paying attention to units, we see the shelf is 24 inches long. Taking this information and writing it in symbols, we find that

Now that we have this inequality, we can forget about books for the time being and solve the inequality. To do this, we multiply both sides by to find that

and simplify to find that

*x* ≤ 32

Now we need to think about books again. Sorry. It'll all be over soon. This answer means Shin can fit up to 32 books on his shelf.

Okay, you can stop thinking about books now. We told you it would fly by.

Algebra could also be used to figure out how many cars you can fit in a parking lot, how many boxes of cereal you can fit on a shelf, how many airplane runways you could fit on a piece of land, or how many full-sized marshmallows you can fit in your mouth without choking. Don't try this at home.

In the next section we will be dealing a lot with specific practical applications of algebra. In the meantime, rest assured that algebra is useful.