Đáp án:
6) \(\left[ \begin{array}{l}
x = 7\\
x = - 11\\
x = 1\\
x = - 5\\
x = - 1\\
x = - 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
1)x + 5 \vdots x + 1\\
\to x + 1 + 4 \vdots x + 1\\
\to 4 \vdots x + 1\\
\to x + 1 \in U\left( 4 \right)\\
\to \left[ \begin{array}{l}
x + 1 = 4\\
x + 1 = - 4\\
x + 1 = 2\\
x + 1 = - 2\\
x + 1 = 1\\
x + 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 3\\
x = - 5\\
x = 1\\
x = - 3\\
x = 0\\
x = - 2
\end{array} \right.\\
2)x + 3 \vdots x - 1\\
\to x - 1 + 4 \vdots x - 1\\
\to 4 \vdots x - 1\\
\to x - 1 \in U\left( 4 \right)\\
\to \left[ \begin{array}{l}
x - 1 = 4\\
x - 1 = - 4\\
x - 1 = 2\\
x - 1 = - 2\\
x - 1 = 1\\
x - 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 5\\
x = - 3\\
x = 3\\
x = - 1\\
x = 2\\
x = 0
\end{array} \right.\\
3)x - 10 \vdots x - 5\\
\to x - 5 - 5 \vdots x - 5\\
\to 5 \vdots x - 5\\
\to x - 5 \in U\left( 5 \right)\\
\to \left[ \begin{array}{l}
x - 5 = 5\\
x - 5 = - 5\\
x - 5 = 1\\
x - 5 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 10\\
x = 0\\
x = 6\\
x = 4
\end{array} \right.\\
4)7 \vdots x + 1\\
\to x + 1 \in U\left( 7 \right)\\
\to \left[ \begin{array}{l}
x + 1 = 7\\
x + 1 = - 7\\
x + 1 = 1\\
x + 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 6\\
x = - 8\\
x = 0\\
x = - 2
\end{array} \right.\\
5) - 5 \vdots x - 1\\
\to 5 \vdots x - 1\\
\to x - 1 \in U\left( 5 \right)\\
\to \left[ \begin{array}{l}
x - 1 = 5\\
x - 1 = - 5\\
x - 1 = 1\\
x - 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 6\\
x = - 4\\
x = 2\\
x = 0
\end{array} \right.\\
6)9 \vdots x + 2\\
\to x + 2 \in U\left( 9 \right)\\
\to \left[ \begin{array}{l}
x + 2 = 9\\
x + 2 = - 9\\
x + 2 = 3\\
x + 2 = - 3\\
x + 2 = 1\\
x + 2 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 7\\
x = - 11\\
x = 1\\
x = - 5\\
x = - 1\\
x = - 3
\end{array} \right.
\end{array}\)
