Question 1015979
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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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<pre>
{{{(4x)/(x-4)}}} = {{{16/(x-4)}}} + {{{5}}}.

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.
</pre>

<U>comment from student</U>: Thanks so much! So would you call this an inconsistent equation?


<pre>
<U>My responce</U>. Yes, it is an inconsistent equation.

(Although, usually the term "inconsisted" is applied in the Shcool Math to systems of equations).
</pre>