None of the provided responses accurately explain why Shawn would multiply both sides of the equation \( x^7 - 47 = -6 \) by 7.
In general, multiplying both sides of an equation by a certain number is a step often used to eliminate fractions or to manipulate the equation for simplification, but in this case, the equation doesn't need to be multiplied by 7 to isolate \( x \) or perform any specific operation.
If Shawn is trying to solve for \( x \), he would typically first add 47 to both sides of the equation to eliminate the -47.
However, if we strictly address the question about the rationale for multiplying by 7, it does not correspond to any of the provided options correctly.
If the question is about the process of isolating the variable or simplifying the equation, a more appropriate response would be "to prepare the equation for easier manipulation." However, that specific option is not provided here.
Ultimately, the best choice among the responses, although not entirely correct, would lean more towards:
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
This reflects a misunderstanding of the original equation but somewhat aligns with the idea of manipulating the equation. However, it's crucial to note that multiplying doesn't actually address anything specific in this case, as \( x^7 - 47 = -6 \) does not involve any division by 7 in the actual problem presented.