2x−1≤x5
Let's find the critical points of the inequality.
2x−1=x^5
2x−1−x^5=x^5−x^5 (Subtract x^5 from both sides)
−x^5+2x−1=0
(−x+1)(x^4+x^3+x^2+x−1)=0 (Factor left side of equation)
−x+1=0 or x^4+x^3+x^2+x−1=0 (Set factors equal to 0)
x=1 or x=0.51879 or x=−1.290649