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ive been puzzled over this problem for hours. can any of you help me. here it is (20/(x-19)) + (-6/(x-18))= 0 what does x equal? its killing me please help...
01-20-2009, 09:13 PM #1
01-20-2009, 09:46 PM #2
20/x-19 + -6/x-18 = 0 Ok, I'm assuming what you have written doesn't have any parentheses, else if it's supposed to be 20/(x-19), the result will change.
First step is to get x on one side of the equals sign, so just add 19 and 18 to both sides... or think of it as moving those numbers to the other side of the equals sign and changing their sign.
20/x + -6/x = 19 + 18
20/x + -6/x = 37
Now, multiply both sides by x. (x/x = 1)
20 + -6 = 37x
And you should be home free...
14 = 37x
x = 14/37
01-20-2009, 10:05 PM #3
01-20-2009, 10:17 PM #4
01-20-2009, 10:21 PM #5
01-20-2009, 10:28 PM #6
01-20-2009, 10:33 PM #7
Ok, so I'll try to walk you thru the steps. That way you can apply them to any problem.
There's several ways to solve it. The key thing is get the numbers into an easy form to work with. Ultimately you want to get x on one side.
So try to get into a form where x is not in the denominator. Think of the parentheses as gathering numbers together.
(20/(x-19)) + (-6/(x-18))= 0
One solution is to move one group to the other side of the equals... (note the sign change)
(20/(x-19)) = (6/(x-18))
Now if I multiply both sides with one of the denominators (for example (x-19)), watch what happens:
(x-19)*20/(x-19) = (x-19)*6/(x-18)
20 = (x-19)*6/(x-18)
Do the same thing with (x-18):
20*(x-18) = (x-18)(x-19)*6/(x-18)
20(x-18) = 6(x-19)
Think of what I did like this: you can make substitutions
A = (x-19)
B = (x-18)
20/A = 6/B
20AB/A = 6AB/B
20B = 6A (now substitute back for A & B)
20(x-18) = 6(x-19)
So in this form, it's easier to work with:
20x -20*18 = 6x -6*19
Now gather x to one side...
20x - 6x = 20*18 - 6*19
And extract x:
x(20 - 6) = 20*18 - 6*19
x(14) = 20*18 - 6*19
x = (20*18 - 6*19)/14
x = 246/14 (if I didn't goof up
Last edited by JnC; 01-20-2009 at 10:33 PM. Reason: Automerged Doublepost
01-20-2009, 10:42 PM #8
01-20-2009, 10:49 PM #9
14x-246 = 7x-123
My take on the problem.
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01-21-2009, 01:33 PM #10
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01-21-2009, 10:30 PM #11