Final answer:
After analyzing the given options and comparing them to the original inequality x − 41 < 57, it is found that none of the options match exactly when simplified. Thus, the correct equivalent inequality cannot be determined from the provided choices.
Step-by-step explanation:
The inequality equivalent to x − 41 < 57 is found by isolating x on one side. First, add 41 to both sides of the inequality to get x < 98. Then, to determine which of the given options is equivalent, we rearrange the options to see if any of them simplify to x < 98. After reviewing the options, none match exactly, but they may be equivalent with further manipulation.
Option A) 9x − 49 < 0 does not simplify to x < 98 on its own. Option B) x − 49 < 9 rearranges to x < 58 when you add 49 to both sides, which is not equivalent to x < 98. Option C) x − 4 − 9 < 0 rearranges to x − 13 < 0 and further to x < 13, which is also not equivalent. Lastly, option D) x − 49 ≤ 9 also rearranges to x ≤ 58, which is similar but not identical due to the non-strict inequality 'less than or equal to' symbol.
Since none of the options perfectly match x < 98, the correct answer cannot be determined from the given options provided in the question.