SOLUTION: The question is If one-half of an integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers? Making the problem

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Question 58557This question is from textbook
: The question is
If one-half of an integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?
Making the problem
3/5x-1/2(x-1)=3
LCF = 10
6/10x-5/10(x-1)=3
6x-5x+5=3
x=-2
But when I try to put that number back into the problem, it doesn't work out. 4 works out, but I don't know how to get there. Can you help? Thanks in advance.
 This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the integer and x+1 = the next consecutive integer.
%283%2F5%29%28x%2B1%29-%281%2F2%29x+=+3 Multiply through by the LCD of 10.
6%28x%2B1%29-5x+=+30 Simplify and solve for x.
6x%2B6-5x+=+30
x%2B6+=+30 Subtract 6 from both sides.
x+=+24
x%2B1+=+25
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Check:
%283%2F5%29%2825%29-%281%2F2%29%2824%29+=+15-12 = 3