Question 251871
let n, m and p be the three  numbers.
 the 3rd is one less than the sum of the other two
p=n+m-1
 It is also 8 more than twice the 2nd.
p=8+2*m
The 1st is one less than 3 times the difference of the 3rd minus the 2nd.
n=3*(p-m)-1 
so our three equations with three unknowns are
p=n+m-1
p=8+2*m
n=3*(p-m)-1 
m = -7,   n = 2,   p = -6
n is the largest since n=2 and the others are negative
check
1-
p=n+m-1
-6=2-7-1
-6=2-8
-6=-6
ok
2-
p=8+2*m
-6=8+2*(-7)
-6=8-14
-6=-6
ok
3-
n=3*(p-m)-1
2=3*(-6-(-7))-1
2=3*(-6+7)-1
2=3*(1)-1
2=3-1
2=2
ok