Find four consecutive integers such that 3 times the sum of the first and third is 84 greater than the opposite of the second.

okay thank you that helps so much 

Find four consecutive integers such that 3 times the sum of the first and third is 84 greater than the opposite of the second.

so it is your consecutive numbers:

$\text{x , x+1 , x+2 , x+3}$

3 times the sum of the first and third is 84 greater than the opposite of the second:

$3\times(x+x+2)=-(x+1)+84 \\ 6x+6=-x+83 \\ 7x=77\\ x=11$

so your numbers are 11, 12, 13, 14

Nice job, Solveit......