0

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?

Eugene
  • 7,612
  • 4
  • 33
  • 66
alistarmk
  • 1
  • 2
    It is quite difficult to read what you have posted.Do you know LaTex? :) –  Jun 24 '12 at 12:43
  • 1
    My guess is that he means to solve $$3-\frac{32}{20-\frac{16}{5-\frac{5}{x}}}=1$$ – nullUser Jun 24 '12 at 13:00
  • @nullUser The answer should be 2. I don't know why Latex is needed in my question. It's just some calculations using PEMDAS. I have no problem with that but what confuses me is the variable x. – alistarmk Jun 24 '12 at 13:34
  • The solution is correct for the equation as parsed above. Is this the original form of the exercise in the book? Your notation is nonstandard and nullUser and I had to guess. – ncmathsadist Jun 24 '12 at 13:39
  • This is why you need LaTeX. It allows you to post your formula in a readily-understandable manner. – ncmathsadist Jun 24 '12 at 13:41
  • @ncmathsadist I have written the exercise exactly as it is in the book. I don't understand why nullUser used fractions. The exercise in the book is exactly as I've written it. I live in EU. – alistarmk Jun 24 '12 at 13:47
  • What is the meaning of the : symbol? – ncmathsadist Jun 24 '12 at 13:54
  • @ncmathsadist : - divide – alistarmk Jun 24 '12 at 14:47
  • There is absolutely no other way to phrase the equation without introducing a "trivial simplification" involving a numerical calculation. The solution is $x=5$ as others have shown and judging by the numbers used I would say the question has been constructed in such a way that this had to be the solution (there are certain nice numbers in there made for cancellations to produce whole numbers). The books solution is almost certainly wrong (I have known this happen many times with many different textbooks). – fretty Jun 24 '12 at 15:01
  • 1
    "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. – Gerry Myerson Jun 25 '12 at 06:32

1 Answers1

2

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 $x = 5.$

ncmathsadist
  • 49,383