This is due tomorrow and I need help quick. Please put an easy, understandale solution.

x = first integer

x+1 = second    x+2 = next etc

x  +  x+1  +  x+2  +  x+3  +  x+4  +  x+5   +  x+6 = 63     gather all of the 'like' terms

7x  + 21=63     subtract 21 from both sides of the equation

7x = 42          divide thru by 7

x = 6 = smallest

x+6 = larges= 6+ 6= 12         6+ 12 = 18

We have: \(x-3, x-2, x-1, x, x+1, x+2, x+3\) . Adding all of these together, we get \(7x=63, x=9\) . The smallest number is \(6 \) and the largest number is \(12.\) Thus, the answer is \(6+12=\boxed{18}.\) (A).

Thanks EP and tertre!