11.1. Solve the inequality $\left|x^{2}-x\right| \leq 2 x^{2}-3 x+1$.
Answer: $x \leq 1 / 3 ; x \geq 1$.

Solution. If $x^{2}-x>0$, i.e., when $x>1$ or $x<0$, the original inequality holds. If $x^{2}-x \leq 0$, i.e., when $0 \leq x \leq 1$, the inequality can be written as: $3 x^{2}-4 x+1 \geq 0 \Leftrightarrow(x-1 / 3)(x-1)$ $\geq 0 \Leftrightarrow x \leq 1 / 3$ or $x \geq 1$. Considering the domain $0 \leq x \leq 1$, we get the answer.