To solve the inequality \( x - 6 < x^4 \), a good first step would be to rearrange the inequality so that all terms are on one side. A well-chosen first step might be:
Move all terms to one side: \[ x - 6 - x^4 < 0 \] which can be rewritten as: \[ -x^4 + x - 6 < 0 \]
Now, regarding the responses provided, trying to multiply by variables (like multiplying both sides by \( x \)) can be tricky because if \( x \) is negative, it reverses the inequality.
Thus, the most straightforward first step would be:
- Move all terms to one side to simplify.
After that, to solve the inequality, we would typically factor or analyze the function \( -x^4 + x - 6 \) to find the points at which it equals zero and determine where it is negative.
The correct solution involves finding the values of \( x \) where \( -x^4 + x - 6 < 0 \).
However, from your options, it seems like the initial viable approach (albeit it wasn't listed) would rather be to manipulate and express the inequality clearly as \( x^4 - x + 6 > 0 \).
I recommend avoiding the attempts that suggest multiplying both sides by \( x \) or a fraction unless \( x \) is constrained to be positive, due to the nature of inequalities.
No exact matches for correct steps are found in your provided options.