SOLUTION: Please help me set up and solve this problem. The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24. What is the integer?

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Question 315244: Please help me set up and solve this problem. The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24. What is the integer?
Found 2 solutions by malaydassharma, ankor@dixie-net.com:
Answer by malaydassharma(59) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be x
So,+1%2F2x+%2B+1%2F%282x%2B2%29=7%2F24
Or,+%282x%2B1%29%2Fx%28x%2B1%29=7%2F12
Or,+7x%5E2-17x-12=0
Or,+7x%5E2-21x%2B4x-12=0
Or,+%287x%2B4%29%28x-3%29=0
Or,+x=3+ and ++x=-4%2F7
x being integer , answer x=3

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24.
What is the integer?
:
Let x = the integer
1%2F%282x%29 + 1%2F%28%282x%2B2%29%29 = 7%2F24
multiply equation by 24x(2x+2)
24x(2x+2)*1%2F%282x%29 + 24x(2x+2)*1%2F%28%282x%2B2%29%29 = 24x(2x+2)*7%2F24
cancel the denominators, results:
12(2x+2) + 24x = 7x(2x+2)
:
24x + 24 + 24x = 14x^2 + 14x
:
48x + 24 = 14x^2 + 14x
:
Combine on the right
0 = 14x^2 + 14x - 48x - 24
:
A quadratic equation
14x^2 - 34x - 24 = 0
:
simplify, divide by 2
7x^2 - 17x - 12 = 0
:
factor this to
(7x+4)(x-3) = 0
:
The positive solution is all we want here
x = 3 is the integer, that everyone is waiting for!
:
:
See if this is true
1%2F%282%2A3%29 + 1%2F%28%282%283%29%2B2%29%29 = 7%2F24
1%2F6 + 1%2F8 = 7%2F24
4%2F24 + 3%2F24 = 7%2F24