Three consecutive integers are x, x+1, x+2. Determine if any integers satisfy the condition: twice the middle integer equals the sum of the other two integers plus 3. If a solution exists, find it; if not, explain why.

No solution exists because the equation simplifies to a false statement.

A solution exists; the integers are 3, 4, and 5.

No solution exists because the sum of the first and third integers already equals twice the middle.

No solution exists because consecutive integers cannot satisfy the condition.