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I need to solve this equation: 4x/x-4 = 16/x-4 + 5
And specify whether it is an identity, a conditional equation, or an inconsistent equation. I am clueless. Any sort of help would be appreciated. Thanks.
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Multiply both sides by (x-4) to rid off the denominators. You will get
4x = 16 + 5*(x-4).
Simplify:
4x = 16 + 5x - 20,
4x - 5x = 16 - 20,
-x = -4.
x = 4.
This is the only possible solution, but it doesn't fit the original equation, because the denominators are zero at x = 4.
The given equation has no solutions.
comment from student: Thanks so much! So would you call this an inconsistent equation?
My responce. Yes, it is an inconsistent equation.
(Although, usually the term "inconsisted" is applied in the Shcool Math to systems of equations).
