<s>[INST] A question about an inequality How to get the solution set of the inequality $$\left ( \frac{\pi}{2} \right )^{(x-1)^2}\leq \left ( \frac{2}{\pi} \right )^{x^2-5x-5}?$$
 [/INST] Multiplying either sides by $\left(\frac\pi2\right)^{(x^2-5x-5)}$
$$\left(\frac\pi2\right)^{(x-1)^2+(x^2-5x-5)}\le 1\iff \left(\frac\pi2\right)^{2x^2-7x-4}\le 1=\left(\frac\pi2\right)^0$$
$\implies 2x^2-7x-4\le0$ as $\pi>2\iff \frac\pi2>1,$
Now, if $(x-a)(x-b)\le0$ where $a\le b,$   $a\le x\le b$
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