consecutive intgers

Question

Three consecutive odd integers exist such that twice the sum of the first two integers, decreased by five is the same as twelve subtracted from five times the third integer. Find the largest integer. Write the integer only

Answer 1

F+S-5 = 5T-12

F=x-2

S=x

T = x+2

2(x-2 + x) -5 = 5(x+2) -12

2(2x-2) -5 = 5x+10-12

4x -4-5 = 5x -2

4x -9 =-5x-2

x = -7

x-2 = -9

x+2 = -5

the numbers are --9, -7 and -5, 3 consecutive odd integers