document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #94993 by checkley71(8403)\"\" \"About 
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THE RECIPROCAL OF 2 TIMES AN INTEGER IS 1/2X
\n" ); document.write( "THE RECIPROCAL OF 2 MORE THAN TWICE THE INTEGER IS 1/(2X+2)
\n" ); document.write( "1/2X+1/(2X+2)=7/24 FIND A COMMON DENOMINATOR FOR THE LEFT TERMS:
\n" ); document.write( "(2+2X+2X)/2X(2X+2)=7/24
\n" ); document.write( "(2+4X)/(4X^2+4X)=7/24 NOW CROSS MULTIPLY:
\n" ); document.write( "7(4X^2+4X)=24(2+4X)
\n" ); document.write( "28X^2+28X=48+96X
\n" ); document.write( "28X^2+28X-96X-48=0
\n" ); document.write( "28X^2-68X-48=0
\n" ); document.write( "4(7X^2-17X-12)=0
\n" ); document.write( "4(7X+4)(X-3)=0
\n" ); document.write( "7X+4=0
\n" ); document.write( "7X=-4
\n" ); document.write( "X=-4/7 ANSWER
\n" ); document.write( "X-3=0
\n" ); document.write( "X=3 ANSWER.
\n" ); document.write( "PROOF:
\n" ); document.write( "1/2*3+1/(2*3+2)=7/24
\n" ); document.write( "1/6+1/8=7/24
\n" ); document.write( "(8+6)/48=7/24
\n" ); document.write( "14/48=7/24
\n" ); document.write( "7/24=7/24 \n" ); document.write( "
\n" );