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 + 1 = second consecutive integer

**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*