
\begin{enumerate}
\item $\begin{aligned}[t]
(4x-5)^2 \leqslant (12x-15)(1-x) &\iff  (4x-5)^2 \leqslant 3(4x-5)(1-x)\\
& \iff (4x-5)^2 - 3(4x-5)(1-x) \leqslant 0\\
& \iff (4x-5)\big[(4x-5)-3(1-x)\big] \leqslant0\\
& \iff (4x-5)(4x-5-3+3x) \leqslant0\\
& \iff (4x-5)(7x-8) \leqslant 0
\end{aligned}$
\begin{center}
\begin{tikzpicture}
\tkzTabInit[lgt=3,deltacl=0.5,espcl=2,color,colorC=numpagecorrige!20,colorL=numpagecorrige!20,colorV=numpagecorrige!20]{$x$/0.8, $4x-5$/.8, $7x-8$/.8, $(4x-5)(7x-8)$/.8}{$-\infty$,$\frac{8}{7}$,$\frac{5}{4}$,$+\infty$}
\tkzTabLine{,-,,-,z,+, }
\tkzTabLine{,-,z,+,,+,}
\tkzTabLine{,+,z,-,z,+,}
\end{tikzpicture}
\end{center}
\[
\boxed{S = \intervFF{\dfrac{8}{7}}{\dfrac{5}{4}}}
\]

\item $\begin{aligned}[t]
3x^3 > 12x & \iff 3x^3 - 12x > 0\\
& \iff 3x(x^2-4)>0\\
& \iff 3x(x-2)(x+2) > 0
\end{aligned}$
\begin{center}
\begin{tikzpicture}
\tkzTabInit[lgt=3,deltacl=0.5,espcl=2,color,colorC=numpagecorrige!20,colorL=numpagecorrige!20,colorV=numpagecorrige!20]{$x$/0.8, $3x$/.8, $x+2$/.8, $x-2$/0.8, $3x(x-2)(x+2)$/.8}{$-\infty$,$-2$,$0$,$2$,$+\infty$}
\tkzTabLine{,-,,-,z,+,,+ }
\tkzTabLine{,-,z,+,,+,,+}
\tkzTabLine{,-,,-,,-,z,+}
\tkzTabLine{,-,z,+,z,-,z,+}
\end{tikzpicture}
\end{center}
\[
\boxed{S = \intervOO{-2}{0} \cup \intervOO{2}{+\infty} }
\]
\end{enumerate}
