SOLUTION: I'm not sure if I have the right equation for this word problem. Could I have some help, thank you. The reciprocal of two times a certain integer plus the reciprocal of 2 more than

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Question 130066: I'm not sure if I have the right equation for this word problem. Could I have some help, thank you. The reciprocal of two times a certain integer plus the reciprocal of 2 more than twice the integer equals 7/24. I have expression 2x+2x=7/24 answer 7/96. Is this right? If not, could I have some help in solving this. Thanks
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE RECIPROCAL OF 2 TIMES AN INTEGER IS 1/2X
THE RECIPROCAL OF 2 MORE THAN TWICE THE INTEGER IS 1/(2X+2)
1/2X+1/(2X+2)=7/24 FIND A COMMON DENOMINATOR FOR THE LEFT TERMS:
(2+2X+2X)/2X(2X+2)=7/24
(2+4X)/(4X^2+4X)=7/24 NOW CROSS MULTIPLY:
7(4X^2+4X)=24(2+4X)
28X^2+28X=48+96X
28X^2+28X-96X-48=0
28X^2-68X-48=0
4(7X^2-17X-12)=0
4(7X+4)(X-3)=0
7X+4=0
7X=-4
X=-4/7 ANSWER
X-3=0
X=3 ANSWER.
PROOF:
1/2*3+1/(2*3+2)=7/24
1/6+1/8=7/24
(8+6)/48=7/24
14/48=7/24
7/24=7/24