Đáp án:
a) \(x \in \emptyset \)
b) x=5
Giải thích các bước giải:
a)
\(\begin{array}{l}
\left| {x - 2} \right| - \left| {x - 4} \right| = 6\\
\to \left[ \begin{array}{l}
x - 2 - \left( {x - 4} \right) = 6\left( {DK:x \ge 4} \right)\\
x - 2 + x - 4 = 6\left( {DK:4 > x \ge 2} \right)\\
- x + 2 + x - 4 = 6\left( {DK:2 > x} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
2 = 6\left( l \right)\\
2x - 6 = 6\\
- 2 = 6\left( l \right)
\end{array} \right.\\
\to 2x = 12\\
\to x = 6\left( l \right)\\
\to x \in \emptyset
\end{array}\)
\(\begin{array}{l}
b)\left| {x - 2} \right| = 2x - 7\\
\to \left[ \begin{array}{l}
x - 2 = 2x - 7\left( {DK:x \ge 2} \right)\\
- x + 2 = 2x - 7\left( {DK:2 > x} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 5\\
3x = 9
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 5\\
x = 3\left( l \right)
\end{array} \right.\\
\to x = 5
\end{array}\)
