Solving an EquationDate: 11/30/2002 at 11:11:59 From: Amanda Parrish Subject: Solving an Equation Dear Dr. Math, In math class we have been assigned to answer the following question: How do you solve an equation? I know how to solve an equation if it is given to me, but I do not know how to describe how to solve any equation. I hope you can help. Thanks, Amanda Parrish Date: 11/30/2002 at 12:00:33 From: Doctor Ian Subject: Re: Solving an Equation Hi Amanda, To solve an equation, you apply inverses to each side of the equation until the variable you want to solve for is alone by itself on one side of the equation, and appears nowhere on the other side. What is an inverse? An inverse is an operation that 'undoes' another operation. Suppose you have something like x + 5 = 10 The additive inverse of 5 is -5, so you can 'invert' the addition by adding -5: x + 5 + -5 = 10 + -5 x = 5 Suppose you have something like 2x = 10 The multiplicative inverse of 2 is 1/2, so you can 'invert' the multiplication by multiplying by 1/2: 2x * (1/2) = 10 * (1/2) x = 5 Suppose you have something like log x = 3 The inverse of a logarithm is an exponent, so you can 'invert' the log by making both sides exponents of the base of the log: log x 3 10 = 10 3 x = 10 And sometimes you have to combine these into multiple steps: log(2x + 5) = 3 log(2x + 5) 3 10 = 10 Invert the log. 2x + 5 = 1000 2x + 5 + -5 = 1000 + -5 Invert the addition 2x = 995 2x * (1/2) = 995 * (1/2) Invert the multiplication x = 995/2 A general question like "How do you solve an equation" deserves a general answer, so I'd probably just restate my initial sentence: To solve an equation, you apply inverses to each side of the equation until the variable you want to solve for is alone by itself on one side of the equation, and appears nowhere on the other side. Obviously which inverses you apply, and the order in which you apply them, depends on the operations that need to be inverted. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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