Đáp án:
k. Phương trình vô nghiệm
Giải thích các bước giải:
\(\begin{array}{l}
a.\left| {2 - x} \right| = 2x - 5\\
\to \left[ \begin{array}{l}
2 - x = 2x - 5\left( {DK:x \le 2} \right)\\
2 - x = - 2x + 5\left( {x > 2} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
3x = 7\\
x = 3
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{7}{3}\left( l \right)\\
x = 3\left( {TM} \right)
\end{array} \right.\\
d.\left| {5x} \right| = 3x + 9\\
\to \left[ \begin{array}{l}
5x = 3x + 9\left( {x \ge 0} \right)\\
5x = - 3x - 9\left( {x < 0} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = 9\\
8x = - 9
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{9}{2}\\
x = - \dfrac{9}{8}
\end{array} \right.\\
e.\left| {3x} \right| = x + 8\\
\to \left[ \begin{array}{l}
3x = x + 8\\
3x = - x - 8
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = 8\\
4x = - 8
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 4\\
x = - 2
\end{array} \right.\\
g.\left| {5x - 4} \right| = 4 - 5x\\
\to \left[ \begin{array}{l}
5x - 4 = 4 - 5x\left( {x \ge \dfrac{4}{5}} \right)\\
5x - 4 = - 4 + 5x\left( {x < \dfrac{4}{5}} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
10x = 8\\
0x = 0\left( {ld} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{4}{5}\\
0x = 0\left( {ld} \right)
\end{array} \right.
\end{array}\)
KL: \(x = \dfrac{4}{5}\) hoặc phương trình có vô số nghiệm với \({x < \dfrac{4}{5}}\)
\(\begin{array}{l}
k.\left| {6x - 7} \right| = 3x - 8\\
\to \left[ \begin{array}{l}
6x - 7 = 3x - 8\left( {x \ge \dfrac{7}{6}} \right)\\
6x - 7 = - 3x + 8\left( {x < \dfrac{7}{6}} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
3x = 1\\
9x = 15
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{1}{3}(l)\\
x = \dfrac{5}{3}(l)
\end{array} \right.
\end{array}\)
⇒ Phương trình vô nghiệm
