Explanation
Correct answer: B.
Choice B is correct. It's given that the minimum value of is less than times another number . Therefore, the possible values of are all greater than or equal to the value of less than times . The value of times is given by the expression . The value of less than is given by the expression . Therefore, the possible values of are all greater than or equal to . This can be shown by the inequality .
Desmos solution:
Note: The expression x ≥ 6n - 12 directly translates the phrase “minimum value of x is 12 less than 6 times n” into an inequality.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. This inequality shows the possible values of if the maximum, not the minimum, value of is less than times .
Choice C
Choice C is incorrect. This inequality shows the possible values of if the maximum, not the minimum, value of is times less than , not less than times .
Choice D
Choice D is incorrect. This inequality shows the possible values of if the minimum value of is times less than , not less than times .