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?
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?
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 $x = 5.$