Question 159119
Let x = first integer.

Then:  x + 1 = second integer and x + 2 = third integer

The least of the integers is x.

We add all three and then equate the sum to x - 47.

Where did x - 47 come from?

In the question we read: "...47 less than the least of the integers."  Since the least of the integers is x, we subtract 47 from the x.

x + x + 1 + x + 2 = x - 47

3x + 3 = x - 47

3x - x = -47 - 3

2x = -50

x = -50/2

x = -25...This is the first integer.

x + 1 = -25 + 1 = -24...This is the second integer.

x + 2 = -25 + 2 = -23...This is the third integer.

Notice that they are consecutive: one comes right after the other.

Did you follow?

P.S. The number -25 the furthest away from zero on the number line.  This is why is the smallest of the three integers.