Final answer:
The correct answer is option (d) which is 14. To reach this conclusion, we establish a relationship based on the consecutive even integers and the given sum condition, solve for x, and find that the first even integer is 14.
Step-by-step explanation:
The question is asking us to find the first of three consecutive even integers given that the sum of the first and second integers is 10 less than three times the third. To find the solution, we'll start by letting x be the first even integer. Then, the second even integer would be x + 2, and the third would be x + 4 because even integers are two units apart.
The relationship given in the problem is x + (x + 2) = 3(x + 4) - 10. Simplifying this equation gives us 2x + 2 = 3x + 12 - 10, which further simplifies to x = 14 after moving terms from one side of the equals sign to the other and combining like terms.
Therefore, the first even integer is 14, which makes option (d) the correct answer.