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Linear Equations in One Variable

```
Date: 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

6 = x - 2

7 = x - 1

8 = x

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Equations

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