In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer

Question

In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer is represented by $x$ . The product of $12$ and the fourth odd integer is at most $26$ less than the sum of the first and third odd integers. Which inequality represents this situation?

A.

$12 (x + 6) \leq x + (x + 4) - 26$

B.

$12 (x + 6) \geq 26 - (x + (x + 4))$

C.

$12 (x + 4) \leq x + (x + 3) - 26$

D.

$12 (x + 4) \geq 26 - (x + (x + 3))$

Accepted Answer

Choice A is correct. It&rsquo;s given that the four odd integers are consecutive, ordered from least to greatest, and that the first odd integer is represented by x . It follows that the second odd integer is represented by x + 2 , the third odd integer is represented by x + 4 , and the fourth odd integer is represented by x + 6 . Therefore, the product of 12 and the fourth odd integer is represented by 12 x + 6 , and 26 less than the sum of the first and third odd integers is represented by x + x + 4 - 26 . Since the product of 12 and the fourth odd integer is at most 26 less than the sum of the first and third odd integers, it follows that 12 x + 6 &le; x + x + 4 - 26 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question 901a91