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