Solving an Equation in One Variable
Date: 12/30/95 at 15:48:12 From: Anonymous Subject: Solving Equations Hi there, I am reviewing for a test coming up. I need you to go step by step with me so I don't miss anything. 2(x+4) - 1= 3 + 4(x-1) I have tried to get this question right, but the signs and the numbers keep fooling me. Thanks, Dr. Math - Dave Amouzouvi Grade 9 Math student in need of desperate help!
Date: 1/4/96 at 11:21:2 From: Doctor Elise Subject: Re: Solving Equations Hi! I hope this isn't too late for your test or that it will help with the next one. If you're having trouble keeping track of your pluses and minuses, the best way to approach these problems is to write EVERY step (and do it really neatly) right underneath the previous one, and don't skip steps or take shortcuts. I had a professor who used to offer us a "box full of minus signs" - all the minus signs that had been dropped from his equations and tests over the years. Everybody does this! Anyhow: 2(x + 4) - 1 = 3 + 4(x - 1) Here's the original problem. 2x + 8 - 1 = 3 + 4x - 4 First, I multiply everything out. 2x + 7 = 4x - 1 Next I simplify by adding or subtracting the numbers without "x" terms in them 2x + 7 - 4x = 4x - 1 - 4x Since I can do anything I want to this equation as long as I do the same thing to both sides, I subtract 4x from each side in order to move the "x" terms to the same side of the equation and add them. -2x + 7 = -1 Here I've simplified the "x" terms -2x + 7 - 7 = -1 -7 Now I subtract 7 from each side to move the remaining numbers without "x" terms to the same side of the equation and add them together. -2x = -8 Of course, I always end up doing this backwards so that everything is negative! It's just as legal an approach, but not as tidy. 2x = 8 I multiplied each side by -1 to get rid of the minus signs. x = 4 I divided each side by 2 to solve for "x". Ta Da! -Doctor Elise, The Math Forum
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