Solving for x
Date: 10/22/96 at 19:57:56 From: Shelby Dotson Subject: Math, Algebra Dear Dr. Math, How do you solve an equation for x? Example: x/a = k I don't get it and I can't find the answer in my book. My friends in algebra 1 don't know either. Please help! Thanks, Shelby Ann Dotson
Date: 10/24/96 at 16:47:8 From: Doctor Rob Subject: Re: Math, Algebra The question is, what expression can you substitute for x and make the equation given true? Can you think of some expression which, when divided by a, gives x? If you can't guess, you can use the following method. You want to change the equation into one of the form x = something. To make (x/a) into x, we need to "undo" the division by a. The operation that does that is multiplication by a, since if we start with any number and divide it by something, then multiply the result by the same something, we get the original number back. Also, if we start with any number and multiply it by something, then divide the result by the same something, we get the original number back again. This tells us that we want to multiply the left side of the equation by a. We can't just do that, however, since we want the equation to still be true. We have to multiply *both* sides of the equation by a. Then, since equals (x/a and k are equals) multiplied by equals (a and a are also equals) give equals, we get (x/a) * a = k * a, or else x = k * a. Does this work? We can check by seeing if putting k a in the equation in place of x gives a true equation: (k a)/a = k is true, all right, since multiplying k by a and dividing by a gives back k. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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