Question 669966
{{{15/27=2x/11}}} is a proportion.
You may have seen only very simple proportions before,
but proportions can get even more complicated.
There could be expressions like {{{2x}}}, or {{{x-5}}}, or worse,
in one or more positions in a proportion.
{{{2x}}} just means {{{2}}} times {{{x}}}.
There is more than one way to solve that proportion, but all will lead to the same result.
If you would solve {{{15/27=y/11}}}
by cross multiplying to get {{{15*11=27*y}}},
You would do kind of the same thing for {{{15/27=2x/11}}}.
You would cross multiply with the {{{2x=2*x}}} treated as a package
From {{{15/27=2x/11}}}, you would cross multiply to get
{{{15*11=27*(2x)}}}
Then,
{{{15*11=27*(2*x)}}} --> {{{165=(27*2)*x)}}} --> {{{165=54*x)}}} --> {{{165/54=54*x/54)}}} --> {{{165/54=x)}}}
Now we can simplify {{{165/54}}} by dividing numerator and denominator by {{{3}}} to get
{{{highlight(x=55/18)}}}