Find three consecutive integers

Find three consecutive integers such that the sum of the first and three times the second is 44 less than five times the third.

x = first consecutive integer
x + 1 = second consecutive integer   {consecutive integers increase by 1}
x + 2 = 3rd consecutive integer

x + 3(x + 1) = 5(x + 2) - 44   {sum of 1st and 3 times 2nd is 44 less than 3 times the 3rd}
x + 3x + 3 = 5x + 10 - 44   {used distributive property}
4x + 3 = 5x - 34   {combined like terms}
3 = x - 34   {subtracted 4x from each side}
x = 37   {added 34 to each side}
x + 1 = 38   {substituted 37, in for x, into x + 1}
x + 2 = 39   {substituted 37, in for x, into x + 2}

37, 38, and 39 are the three consecutive integers

- Algebra House