Three times the greatest of three consecutive even integers exceeds twice the least by 38. find the integers

The three numbers are 32,33, and 34.

Step-by-step explanation:

Let the three consecutive integers be for any integer .

Integers are numbers in the set: .

We are given that '3 times greatest of these numbers exceeds 2 times the smallest of these numbers by 38'.

This means as an equation we have:

.

Let's solve the above equation.

Distribute:

Combine like terms on the sides:

Subtract on both sides:

Subtract 3 on both sides:

Now let's find and given that :

So the three numbers are 32,33, and 34.

Let's check.

3(greatest)=3(34)=102

2(least)=2(32)=64

Now let's see if 102 is 38 more than 64.

Since 38+64=102, it is.