Find the largest of three consecutive integers such that 3 times the sum of the first and the third integer is equal to 30 more than 4 times the second integer.

Consecutive numbers are numbers that increase or reduce by 1 step.

Let the first consecutive number be x.

So the three consecutive number in increasing order are:

x, x + 1, x + 2

Notice each is increase of 1.

3*(Sum of 1st and 3rd) = 4*second + 30

3*(x + x + 2) = 4*(x+1) + 30

3*(2x + 2) = 4*x + 4*1 + 30

3*2x + 3*2 = 4x + 4 + 30

6x + 6 = 4x + 34             

Simplify by taking the xs to one side and leaving the numbers on the other side

6x - 4x = 34 - 6

2x = 28              Divide by 2

x = 28/2

x = 14

Recall the largest of the consecutive number = x + 2,          x = 14

Largest = x + 2 = 14 + 2 = 16

Largest = 16

I hope this helps.