Đáp án:
$\begin{array}{l}
1)2x + 7 < - 1\\
\Leftrightarrow 2x < - 1 - 7\\
\Leftrightarrow 2x < - 8\\
\Leftrightarrow x < \frac{{ - 8}}{2}\\
\Leftrightarrow x < - 4\\
Vậy\,x < - 4\\
2) - \frac{2}{{3y + 2}} = 3\\
\Leftrightarrow 3y + 2 = - \frac{2}{3}\\
\Leftrightarrow 3y = - \frac{2}{3} - 2\\
\Leftrightarrow 3y = - \frac{8}{3}\\
\Leftrightarrow y = \frac{{ - 8}}{{3.3}} = \frac{{ - 8}}{9}\\
Vậy\,y = \frac{{ - 8}}{9}\\
3)u + v < 0\\
\Leftrightarrow u < - v\\
4)u.\left( {u + 1} \right) \le 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
u \le 0\\
u + 1 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
u \ge 0\\
u + 1 \le 0
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
u \le 0\\
u \ge - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
u \ge 0\\
u \le - 1
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow - 1 \le u \le 0\\
Vậy\, - 1 \le u \le 0
\end{array}$