Linear Equations in One VariableDate: 10/11/2001 at 10:00:16 From: Rebecca England Subject: Solving Linear Equations In One Variable 35 = 17 + 3(x-2) Date: 10/11/2001 at 13:28:24 From: Doctor Ian Subject: Re: Solving Linear Equations In One Variable Hi Rebecca, Let's imagine that the equals sign is a balance beam: 35 17 + 3(x - 2) _________ _____________ ^ = (That's not a bad way to think of it, actually.) We can subtract 1 from each side without changing the balance, right? 34 = 16 + 3(x - 2) And we can keep doing that, 33 = 15 + 3(x - 2) 32 = 14 + 3(x - 2) . . 19 = 1 + 3(x - 2) 18 = 3(x - 2) Of course, we could have accomplished the same thing in one step by subtracting 17 from each side, but this lets you see _why_ that works. Anyway, so now we have this: 18 = 3(x - 2) which is really the same as this: 6 + 6 + 6 = (x - 2) + (x - 2) + (x - 2) So it's pretty clear that each (x-2) corresponds to a 6, right? Which means that 6 = (x - 2) Again, we could have divided both sides by 3, but this shows you _why_ that little trick works. So now, can you think of a number such that, when you subtract 2 from it, you get 6? If not, we can try our first trick again, except adding 1 instead of subtracting 1: 6 = x - 2 7 = x - 1 8 = x I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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