How do I solve an equation with a variable in the numerator?

  • Thread starter AVReidy
  • Start date
  • #1
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Homework Statement



I just missed a 16-point question on a quiz because I didn't know how to separate the variable. It was an absolute value equation, but I just need to know how to deal with a variable in a fraction. Here's what it looked like:

Homework Equations



(5x+10)/2 = 20

The Attempt at a Solution


I tried multiplying everything by the denominator, but I'm not sure if or why that works. Any help would be greatly appreciated, thanks!
 

Answers and Replies

  • #2
Borek
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Multiplying by denominator should work. You can do anything that doesn't change the equality - that means adding, subtracting, multiplying or dividing both sides of the equation by the same thing.

Or you could write the fraction as [itex]\frac {5x}{2} + \frac {10}{2}[/itex].
 
  • #3
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Thanks!
 
  • #4
J2R
2
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The easiest way is to multiply both sides of the equation by the denominator. The reason why this works is because it doesn't change the equality.

(5x+10)/2 = 20
5x+10 = 40
5x = 30
x = 6

Even if the variable was in the denominator, you can still solve for the variable using the same steps.

2/(5x+10) = 20
2 = 100x + 200
-198 = 100x
-198/100 = x
x = -99/50
 

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