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# Equations and Inequalities

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# Solving Equations with One Variable

The process of finding all solution(s) to an equation is called "solving the equation." Solving an equation is like solving a crime—you need to make like Sherlock Holmes and collect your clues, analyze them, and deduce their meanings. Fortunately, we're referring to the Sherlock Holmes from Sir Arthur Conan Doyle's stories, not the one in the feature films, so you probably won't need to deliver any uppercuts.

To solve an equation, we transform it into simpler equivalent equations until we can easily read off the value(s) of the variable that make the equation true. Usually we'd like to get the variable all by its lonesome on one side of the equation, with a number on the other side.

That's the ideal scenario, anyway, but sometimes it becomes tricky. Luckily, "tricky" is our middle name. Shmoop "Tricky" Aagaard. It's Norwegian.

An equation makes a claim that two quantities are equal. It's like saying, for example, that a dozen hockey players *is* twelve hockey players. Never mind what they're all doing on the ice at once. If we put each quantity in one pan of a balance scale, the scale will balance.