Giải thích các bước giải:
a) Ta có:
$\begin{array}{l}
\dfrac{{x - 1}}{5} = \dfrac{{y - 2}}{3} = \dfrac{{z - 1}}{4}\\
\Rightarrow \dfrac{{x - 1}}{5} = \dfrac{{y - 2}}{3} = \dfrac{{z - 1}}{4} = \dfrac{{2\left( {x - 1} \right) - 3\left( {y - 2} \right) - 2\left( {z - 1} \right)}}{{2.5 - 3.3 - 2.4}}\\
= \dfrac{{2x - 3y - 2z + 6}}{{ - 7}}\\
= \dfrac{{ - 27 + 6}}{{ - 7}}\\
= 3\\
\Rightarrow \left\{ \begin{array}{l}
x - 1 = 15\\
y - 2 = 9\\
z - 1 = 12
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 16\\
y = 11\\
z = 13
\end{array} \right.\\
\Rightarrow \left( {x;y;z} \right) = \left( {16;11;13} \right)
\end{array}$
Vậy $\left( {x;y;z} \right) = \left( {16;11;13} \right)$
$\begin{array}{l}
b)3\left| {1 - \dfrac{1}{2}x} \right| = \dfrac{4}{5}\left( {4x - 1} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
4x - 1 \ge 0\\
\left[ \begin{array}{l}
3\left( {1 - \dfrac{1}{2}x} \right) = \dfrac{4}{5}\left( {4x - 1} \right)\\
3\left( {1 - \dfrac{1}{2}x} \right) = - \dfrac{4}{5}\left( {4x - 1} \right)
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge \dfrac{1}{4}\\
\left[ \begin{array}{l}
\dfrac{{47}}{{10}}x = \dfrac{{19}}{5}\\
\dfrac{{17}}{{10}}x = \dfrac{{ - 11}}{5}
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge \dfrac{1}{4}\\
\left[ \begin{array}{l}
x = \dfrac{{38}}{{47}}\left( c \right)\\
x = \dfrac{{ - 22}}{{17}}\left( l \right)
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow x = \dfrac{{38}}{{47}}
\end{array}$
Vậy $x = \dfrac{{38}}{{47}}$
