

\begin{enumerate}
\item $\dfrac{1}{x} \geqslant 81 \iff x \in\intervOF{0}{\dfrac{1}{81}}$.
\begin{center}
\begin{tikzpicture}[>=latex]
\draw[thick,->] (-4,0) -- (4,0);
\draw[thick,->] (0,-4) -- (0,4);
\clip (-4,-4) rectangle (4,4);
\draw plot[domain=-4:-0.1,samples=70] (\x,{1/\x});
\draw plot[domain=0.1:4,samples=70] (\x,{1/\x});
\draw[red,thick] plot[domain=0.1:0.5,samples=70] (\x,{1/\x});
\draw[dashed,orange] (-4,2) -- (4,2);
\node[orange,above left] at (0,2) {$81$};
\draw[dashed,orange] (0.5,2) -- (0.5,0) node[below] {$\frac{1}{81}$};
\end{tikzpicture}
\end{center}

\item $\dfrac{1}{x} < -1 \iff x \in\intervOO{-1}{0}$.
\begin{center}
\begin{tikzpicture}[>=latex,scale=0.8]
\draw[thick,->] (-4,0) -- (4,0);
\draw[thick,->] (0,-4) -- (0,4);
\clip (-4,-4) rectangle (4,4);
\draw plot[domain=-4:-0.1,samples=70] (\x,{1/\x});
\draw plot[domain=0.1:4,samples=70] (\x,{1/\x});
\draw[red,thick] plot[domain=-1:-0.1,samples=70] (\x,{1/\x});
\draw[dashed,orange] (-4,-1) -- (4,-1);
\node[orange,below right] at (0,-1) {$-1$};
\draw[dashed,orange] (-1,-1) -- (-1,0) node[above] {$-1$};
\end{tikzpicture}
\end{center}


\item $\dfrac{1}{x}>-5 \iff x\in\intervOO{-\infty}{-\dfrac{1}{5}}\cup\intervOO{0}{+\infty}$.
\begin{center}
\begin{tikzpicture}[>=latex,scale=0.8]
\draw[thick,->] (-4,0) -- (4,0);
\draw[thick,->] (0,-4) -- (0,4);
\clip (-4,-4) rectangle (4,4);
\draw plot[domain=-4:-0.1,samples=70] (\x,{1/\x});
\draw[thick,red] plot[domain=0.1:4,samples=70] (\x,{1/\x});
\draw[red,thick] plot[domain=-4:-0.5,samples=70] (\x,{1/\x});
\draw[dashed,orange] (-4,-2) -- (4,-2);
\node[orange,below right] at (0,-2) {$-5$};
\draw[dashed,orange] (-0.5,-2) -- (-0.5,0) node[above] {$-\frac{1}{5}$};
\end{tikzpicture}
\end{center}

\item $\dfrac{1}{x} \leqslant 64 \iff x\in\intervOO{-\infty}{0}\cup\intervFO{\dfrac{1}{64}}{+\infty}$.
\begin{center}
\begin{tikzpicture}[>=latex,scale=0.8]
\draw[thick,->] (-4,0) -- (4,0);
\draw[thick,->] (0,-4) -- (0,4);
\clip (-4,-4) rectangle (4,4);
\draw[red,thick] plot[domain=-4:-0.1,samples=70] (\x,{1/\x});
\draw plot[domain=0.1:4,samples=70] (\x,{1/\x});
\draw[red,thick] plot[domain=0.5:4,samples=70] (\x,{1/\x});
\draw[dashed,orange] (-4,2) -- (4,2);
\node[orange,above left] at (0,2) {$64$};
\draw[dashed,orange] (0.5,2) -- (0.5,0) node[below] {$\frac{1}{64}$};
\end{tikzpicture}
\end{center}
\end{enumerate}
