Question 67981
Problem: "The difference of a number and twice its reciprocal is 47/7. Find the number."

My problem is, how can I construct an equation out of the given problem.
I initially tried x-(2)1/x=47/7, but I've got the wrong results.

I think you're on the right track:
{{{x-(2)(1/x)=47/7}}}
{{{x-2/x=47/7}}}  Multiply everything by the LCD, 7x.
{{{7x(x)+7x(-2/x)=7x(47/7)}}}
{{{7x^2-14=47x}}}
{{{7x^2-47x-14=47x-47x}}}
{{{7x^2-47x-14=0}}} Factor
{{{7x^2-49x+2x-14=0}}}
{{{7x(x-7)+2(x-7)=0}}}
{{{(7x+2)(x-7)=0}}}  Set each parentheses = to 0 and solve for x.
7x+2=0 or x-7=0
7x+2-2=0-2 or x-7+7=0+7
7x=-2 or x=7
7x/7=-2/7 or x=7
{{{highlight(x=-2/7)}}} or {{{highlight(x=7)}}}
Sanity check:
{{{-2/7-2(1/(-2/7))=47/7}}}
{{{-2/7-2(-7/2)=47/7}}}
{{{-2/7+7=47/7}}}
{{{-2/7+49/7=47/7}}}
{{{(-2+49)/7=47/7}}}
{{{47/7=47/7}}} x=-2/7 works
{{{7-2(1/7)=47/7}}}
{{{7-2/7=47/7}}}
{{{49/7-2/7=47/7}}}
{{{(49-2)/7=47/7}}}
{{{47/7=47/7}}} x=7 also works
Happy Calculating!!!!