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?

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) (Show Source): You can put this solution on YOUR website!
Let the number be x
So,
Or,
Or,
Or,
Or,
Or, and
x being integer , answer x=3
Answer by ankor@dixie-net.com(22740) (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
+ =
multiply equation by 24x(2x+2)
24x(2x+2)* + 24x(2x+2)* = 24x(2x+2)*
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
+ =
+ =
+ =
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