Rút gọn M=|1$\frac{1}{5}$ – x|+|x- $\frac{1}{5}$ |-3 $\frac{1}{5}$ trong các trường hợp sau: a, x ≥ 1$\frac{1}{5}$ b, x ≤$\frac{1}{5}$ c, $\frac{1}{

Đáp án:

$\begin{array}{l}
a)x \ge 1\dfrac{1}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
\left| {1\dfrac{1}{5} – x} \right| = x – 1\dfrac{1}{5}\\
\left| {x – \dfrac{1}{5}} \right| = x – \dfrac{1}{5}
\end{array} \right.\\
 \Rightarrow M = x – 1\dfrac{1}{5} + x – \dfrac{1}{5} – 3\dfrac{1}{5}\\
 = 2x – 4\dfrac{1}{5} – \dfrac{1}{5}\\
 = 2x – \dfrac{{22}}{5}\\
b)x \le \dfrac{1}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
\left| {1\dfrac{1}{5} – x} \right| = 1\dfrac{1}{5} – x\\
\left| {x – \dfrac{1}{5}} \right| = \dfrac{1}{5} – x
\end{array} \right.\\
 \Rightarrow M = 1\dfrac{1}{5} – x + \dfrac{1}{5} – x – 3\dfrac{1}{5}\\
 =  – 2x – 2\dfrac{1}{5} + \dfrac{1}{5}\\
 =  – 2x – 2\\
c)\dfrac{1}{5} < x < 1\dfrac{1}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
\left| {1\dfrac{1}{5} – x} \right| = 1\dfrac{1}{5} – x\\
\left| {x – \dfrac{1}{5}} \right| = x – \dfrac{1}{5}
\end{array} \right.\\
 \Rightarrow M = 1\dfrac{1}{5} – x + x – \dfrac{1}{5} – 3\dfrac{1}{5}\\
 =  – 2\dfrac{1}{5} – \dfrac{1}{5} = \dfrac{{ – 12}}{5}
\end{array}$