SOLUTION: The lesser of two consecutive even integers is 10 more than one-half the greater. What are the integers?

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Question 110886: The lesser of two consecutive even integers is 10 more than one-half the greater. What are the integers?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the lesser of two consecutive even integers is 10 more than one-half+the+greater, then we have:

If n is an integer than 2n and +2n%2B2 will be two even consecutive integers where 2n is lesser, and 2n+%2B+2 is greater even integer.
If the lesser of two consecutive even integers is 10 more than one-half+the+greater, then we have:
2n++%2B+10+=%281%2F2%29%28+2n+%2B+2%29……..solve for n
2n++%2B+10+=%281%2F2%292n+%2B+2%281%2F2%29%29……..
2n++%2B+10+=+n+%2B+1%29……..move n to the left and 10+ to the right
2n++-n++=+-10+%2B+1%29……..
n++=+-+9%29……..
Then:
the first even number is 2n+=+2%28-9%29+=+-+18, and second even number is 2n+%2B+2+=+-18+%2B+2+=+-+16
check if the lesser of two consecutive even integers is 10 more than one-half+the+greater:
2n++%2B+10+=%281%2F2%29%28+2n+%2B+2%29……..plug in values
-18++%2B+10+=%281%2F2%29%28+-16%29……..
-8+++=+-+8……..