Đáp án:
a) \(\left[ \begin{array}{l}
x = - 22\\
x = 48\\
x = 6\\
x = 20\\
x = 8\\
x = 18\\
x = 12\\
x = 14
\end{array} \right.\)
Giải thích các bước giải:
a) Do 3x-4 là bội của 13-x
\(\begin{array}{l}
\to 3x - 4 \vdots 13 - x\\
\to - 3\left( { - x + 13} \right) + 35 \vdots 13 - x\\
\to 35 \vdots 13 - x\\
\to 13 - x \in U\left( {35} \right)\\
\to \left[ \begin{array}{l}
13 - x = 35\\
13 - x = - 35\\
13 - x = 7\\
13 - x = - 7\\
13 - x = 5\\
13 - x = - 5\\
13 - x = 1\\
13 - x = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = - 22\\
x = 48\\
x = 6\\
x = 20\\
x = 8\\
x = 18\\
x = 12\\
x = 14
\end{array} \right.\\
b)45 - 4x \vdots 5 - 6x\\
\to 135 - 12x \vdots 5 - 6x\\
\to 2\left( {5 - 6x} \right) + 125 \vdots 5 - 6x\\
\to 125 \vdots 5 - 6x\\
\to 5 - 6x \in U\left( {125} \right)\\
\to \left[ \begin{array}{l}
5 - 6x = 125\\
5 - 6x = 25\\
5 - 6x = 5\\
5 - 6x = 1\\
5 - 6x = - 1\\
5 - 6x = - 5\\
5 - 6x = - 25\\
5 - 6x = - 125
\end{array} \right. \to \left[ \begin{array}{l}
x = - 20\\
x = - \dfrac{{10}}{3}\\
x = 0\\
x = \dfrac{2}{3}\\
x = 1\\
x = \dfrac{5}{3}\\
x = 5\\
x = \dfrac{{65}}{3}
\end{array} \right.
\end{array}\)
