
\begin{enumerate}
\item $|x-8|\leqslant3\iff x\in\intervFF{8-3}{8+3}\iff \underline{x\in\intervFF{5}{11}}$.

\item $|x-7|<7\iff x\in\intervOO{7-7}{7+7}\iff \underline{x\in\intervOO{0}{14}}$.

\item $\begin{aligned}[t]
|x+4|\leqslant4 & \iff |x-(-4)|\leqslant4\\
& \iff x\in\intervFF{-4-4}{-4+4}\\
& \iff \underline{x\in\intervFF{-8}{0}}.
\end{aligned}$

\item $\begin{aligned}[t]
|2x-8|\leqslant10 & \iff |2(x-4)|\leqslant10\\
& \iff 2|x-4|\leqslant10\\
& \iff |x-4|\leqslant5\\
& \iff x\in\intervFF{4-5}{4+5}\\
& \iff \underline{x\in\intervFF{-1}{9}}.
\end{aligned}$

\item $\begin{aligned}[t]
|3x+9|<12 & \iff |3(x+3)| < 12\\
& \iff 3|x+3| < 12\\
& \iff |x+3| < 4\\
& \iff |x-(-3)|<4\\
& \iff x\in\intervOO{-3-4}{-3+4}\\
& \iff \underline{x\in\intervOO{-7}{1}}.
\end{aligned}$

\item $\begin{aligned}[t]
|7x-21|<14 &\iff 7|x-3| < 14\\
& \iff |x-3|<2\\
& \iff x\in\intervOO{3-2}{3+2}\\
& \iff \underline{x\in\intervOO{1}{5}}.
\end{aligned}$
\end{enumerate}
