Equations and Inequalities
Introduction to :
One of the nice things about solving equations is that we can check our answers without a solution key. When we solve an equation, we get a value that is supposed to be a solution to the equation. To check our answer, we see whether the value we found is the solution it is supposed to be. (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!")
Recall how this 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 we have 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 equality.
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.
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. 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 when evaluated at y = 5, y = 5 really is the solution to the equation. This is remarkably impressive, considering it is nearly impossible to get those two sides to agree on anything.