Solve for g...

Date: 04/08/97 at 17:44:54
From: Amanda
Subject: Solve for g...

I understand -3x+5x+4 = -6 to solve for x, but I don't understand 
g+.04g+60 = 8796.

Date: 04/09/97 at 13:04:09
From: Doctor Mike
Subject: Re: Solve for g...

Dear Amanda, 
  
Believe it or not, you do the same thing for both problems. 

I'm sure you have seen the Distributive Law, though perhaps you don't 
call it by name all the time.  There are several versions of it.  The 
version "(A + B)*C = A*C + B*C" is the one you need here.  You can 
think of this as telling you how to "multiply out" (A + B)*C , or you 
can think of it as telling you how to "factor out a C" from A*C + B*C.  
That is what is needed here. Let's do a side-by-side for these 2 :
   
Original equation :  
              -3x + 5x + 4 = -6         g + .04g + 60 = 8796

Factor out the unknown (remember, g is 1*g): 
              (-3+5)*x + 4 = -6        (1+.04)*g + 60 = 8796
  
Simplify inside parentheses : 
               (2)*x + 4 = -6           (1.04)*g + 60 = 8796
   
Subtract the right number from both sides: 
               2*x = -10                 1.04*g = 8736  
  
Divide both sides by the coefficient of the unknown: 
               x = -10/2                 g = 8736/1.04
               x = -5                    g = 8400
  
Maybe you just got confused because there were not simple small
numbers used in the second problem, or perhaps because they used 
"g" instead of "x".  Always look for a pattern.
   
I hope this helps.   

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/