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The reciprocal of two times a certain integer plus the reciprocal of 2 more than twice the integer equals 7 divided by 24?
Wiki User
∙ 7y ago
3 AND -4/7 are solutions to the equation (but because the question asked for the integer that satisfies the equation only 3 is correct since -4/7 is not an integer).
Let x be the number. Solve the following equation for x:
(1/2x)+(1/(2x+2))=7/24 [Now you need a common denominator on the left side, so and multiply the second term by (2x) in the numerator and the denominator.]
(2x+2)/(2x(2x+2))+(2x/(2x(2x+2))=7/24 [Now multiply both sides by (2x(2x+2)) and 24 to clear the denominators on both sides.]
24*(2x+2+2x)=7*2x(2x+2) [Multiply out the left and right sides and combine terms to simplify.]
96x+48=28x2+28x [Divide both side by four and solve the quadratic equation.]
24x+12=7x2+7x
7x2-17x-12=0 [The easiest way to solve this (if the factorization is not obvious) is to us the quadratic equation.]
x=(17+/-sqrt(172-4*7*(-12)))/(2*7)
x=(17+/-sqrt(289+336))/(14)
x=(17+/-25)/(14)
x=42/14=3 OR x=-8/14=-4/7
Instead of the quadratic equation, you can observe that the above quadratic equation can be factored into:
(x-3)(7x+4)=0, which yields the same solutions.
The A+ answer is 3.
Wiki User
∙ 7y ago
Wiki User
∙ 9y agoApart from the fact that there is no such thing as an "interger", the above appears to be a mathematical statement - with a question mark stuck at the end. Yes, it does have a solution in the set of real numbers. I presume that answers the question - which you did not bother to ask.
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