Set up an equation that models the numbers Lucas is trying to find

Question

Lucas is trying to find three consecutive, positive integers such that five times the largest is equal to the sum of the smaller two integers

Answer 1

5L = (M+S)

S=x, M=x+2, L=x+4

5(x+4) =x +x +2

5x +20 = 2x +2

3x = 2-20 = -18

x =-18/3 = -6

there are 3 consecutive negative integers: -6,-4 and -2 that satisfy the conditions

but there are no three consecutive odd integers that satisfy the given conditions

solution is the null set