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Answer:
The largest even integer is <u>14</u>.
Step-by-step explanation:
Given:
Three times the second of three consecutive even integers is twelve less than twice the sum of the first and third integers.
Now, to find the largest even integers.
As, 2 is an even number.
Let an even integer be
So, the three consecutive even integers are:
Now, we have to add two to get next even number.
Thus, 3 times the second one of these is:
Now, the sum of the first and third ones are:
So, the twice the sum of the first and third integers is less than twelve:
Now, 3 times the second is 12 less than twice the sum of the other two:
<em>Getting the variables on one side and the number on other:</em>
<em>Dividing both sides by 2 we get:</em>
Now, the even numbers we get are:
<em>Thus, the third number is the largest number which is 14.</em>
Therefore, the largest even integer is 14.