Question

x^4 - x <= 0
Solve the inequality and graph the solution on the real line

Answer 1

add x to both sides.
x^4<=x
take the log of both sides
4lnx<=ln x


Now consider when x is between zero and 1.0

divide by ln x (since it is negative, the signs switch direction)
4>=1 so means all values of x between zero and 1 are valid
Now when x>1
4<=1, which is impossible, so no value of x >1 allowed.
Now when x<0, ln of x is not defined for negative numbers.

so the domain allowed is from zero to one.
Check my thinking.