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### Solving an Equation in One Variable

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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!
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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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Associated Topics:
Middle School Equations

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