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At a Glance - Checking Answers


One of the nice things about solving equations is that we can check our answers without sneaking into the principal's office to nab the solution key. When we solve an equation, we get a value that's supposed to be a solution to the equation. To check our answer, we stick that solution back into the equation and see if it makes the equation true. If not, you can rip off its mask and expose it for the fraud that it really is. "I would have gotten away with it, too, if it wasn't for you meddling kids!"

Here's how it works: we evaluate the left-hand side of the equation at the given value, evaluate the right-hand side of the equation at the given value, and see if the numbers match. We sometimes call this the "plug and chug" method. Plug in the value you found for the variable, and chug out the answer by simplifying the expressions on both sides of the equation.

You can also employ the "plug and chug and hug" method, which involves warmly embracing the correct answer. This one's not for you germaphobes out there.

Sample Problem

Solve the equation 3 = y – 2. Check your answer.

To solve the equation, add 2 to both sides to find that 5 = y. To check the answer, we look to see if 5 really is a solution to the equation 3 = y – 2. That means it's plug and chug time: go back to the original equation and plug in y = 5.

3 = y – 2
3 = (5) – 2
3 = 3

The left-hand side of the equation is 3. The right-hand side evaluated at y = 5 is 5 – 2 = 3. Since the left-hand side and right-hand side agree with each other, y = 5 really is the solution to the equation. This is remarkably impressive, considering it's nearly impossible to get those two sides to agree on anything. 

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