Đáp án:
a. \(\left[ \begin{array}{l}
x = - \dfrac{3}{2}\\
x = - \dfrac{1}{4}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.\left| {x - 1} \right| = 3x + 2\\
\to \left[ \begin{array}{l}
x - 1 = 3x + 2\\
x - 1 = - 3x - 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = - 3\\
4x = - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = - \dfrac{3}{2}\\
x = - \dfrac{1}{4}
\end{array} \right.\\
b.\left| {3x - 1} \right| = x - 2\\
\to \left[ \begin{array}{l}
3x - 1 = x - 2\\
3x - 1 = - x + 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = - 1\\
4x = 3
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = - \dfrac{1}{2}\\
x = \dfrac{3}{4}
\end{array} \right.\\
c.\left| {x + 15} \right| = 3x - 1\\
\to \left[ \begin{array}{l}
x + 15 = 3x - 1\\
x + 15 = - 3x + 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = 16\\
4x = - 14
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 8\\
x = - \dfrac{7}{2}
\end{array} \right.\\
d.\left| {3x - 2} \right| = x + 1\\
\to \left[ \begin{array}{l}
3x - 2 = x + 1\\
3x - 2 = - x - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = 3\\
4x = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{3}{2}\\
x = \dfrac{1}{4}
\end{array} \right.\\
e.\left| {x + 7} \right| = 7 + x\\
\to \left[ \begin{array}{l}
x + 7 = x + 7\left( {ld} \right)\\
x + 7 = - x - 7
\end{array} \right.\\
\to 2x = - 14\\
\to x = - 7
\end{array}\)
