SOLUTION: 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 tr

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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.
Thank you for helping me with this problem.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
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-%282%29%281%2Fx%29=47%2F7
x-2%2Fx=47%2F7 Multiply everything by the LCD, 7x.
7x%28x%29%2B7x%28-2%2Fx%29=7x%2847%2F7%29
7x%5E2-14=47x
7x%5E2-47x-14=47x-47x
7x%5E2-47x-14=0 Factor
7x%5E2-49x%2B2x-14=0
7x%28x-7%29%2B2%28x-7%29=0
%287x%2B2%29%28x-7%29=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%28x=-2%2F7%29 or highlight%28x=7%29
Sanity check:
-2%2F7-2%281%2F%28-2%2F7%29%29=47%2F7
-2%2F7-2%28-7%2F2%29=47%2F7
-2%2F7%2B7=47%2F7
-2%2F7%2B49%2F7=47%2F7
%28-2%2B49%29%2F7=47%2F7
47%2F7=47%2F7 x=-2/7 works
7-2%281%2F7%29=47%2F7
7-2%2F7=47%2F7
49%2F7-2%2F7=47%2F7
%2849-2%29%2F7=47%2F7
47%2F7=47%2F7 x=7 also works
Happy Calculating!!!!