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Solve for $x$:

$3-\frac{32}{20-\frac{16}{5-\frac{5}{x}} }=1$

When I see exercises like this one I panic because I can't figure out what to do with that variable x. What are the steps in solving an exercise like this one?

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    "The answer should be 2." Have you tried putting in 2 for $x$ to see whether it makes the left side equal the right side? If it doesn't, then 2 isn't the answer, whether it "should be" or not.2012-06-25

1 Answers 1

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Strip off the layers, one at a time, to bare the $x$. Begin with $3 - {32\over{20 - {16\over 5 - 5/x}}}=1$ Do a $3-$ on both sides to get $ {32\over{20 - {16\over 5 - 5/x}}} = 2.$ Multiply both sides by the denominator and you have $40 - {32\over 5 - 5/x} = 32 $ Now do a $40 -$ on both sides to obtain ${32\over 5 - 5/x} = 8.$ Multiply both sides by the denominator and factor out the 5 to get $32 = 8\cdot 5(1 - 1/x). $ Divide by 40 and we get ${4\over 5} = 1 - 1/x.$ Do a $1-$ on both sides to see that $1/x = 1/5$. We have $x = 5.$

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    The poser of the question has provided no other interpretation. We have done the best we could with it.2012-06-25