Đáp án:
4) \(\left[ \begin{array}{l}
x = 1\\
x = - 1
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\left| {2 - x} \right| + 2\left| {x + 1} \right| = 4\\
\to \left[ \begin{array}{l}
2 - x + 2x + 2 = 4\left( {DK:2 \ge x \ge - 1} \right)\\
- 2 + x + 2x + 2 = 4\left( {DK:x > 2} \right)\\
2 - x - 2x - 2 = 4\left( {DK:x < - 1} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\left( {TM} \right)\\
3x = 4\\
- 3x = 4
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
x = \dfrac{4}{3}\left( l \right)\\
x = - \dfrac{4}{3}\left( {TM} \right)
\end{array} \right.\\
2)\left| {x + 2} \right| = 2 + \left| {x + 4} \right|\\
\to \left[ \begin{array}{l}
x + 2 = 2 + x + 4\left( {DK:x \ge - 2} \right)\\
- x - 2 = 2 + x + 4\left( {DK: - 2 > x \ge - 4} \right)\\
- x - 2 = 2 - x - 4\left( {DK:x < - 4} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
0 = 4\left( l \right)\\
2x = - 8\\
- 4 = - 4\left( {ld} \right)
\end{array} \right.\\
\to x = - 4\\
3)3\left| {x - 1} \right| + 2\left| {2 - x} \right| = 5\\
\to \left[ \begin{array}{l}
3x - 3 + 4 - 2x = 5\left( {DK:2 \ge x \ge 1} \right)\\
- 3x + 3 + 4 - 2x = 5\left( {DK:x < 1} \right)\\
3x - 3 - 4 + 2x = 5\left( {DK:x > 2} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 4\\
- 5x = - 2\\
5x = 12
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 4\left( l \right)\\
x = \dfrac{2}{5}\left( {TM} \right)\\
x = \dfrac{{12}}{5}\left( {TM} \right)
\end{array} \right.\\
4)\left| {x + 1} \right| + \left| {x - 1} \right| = 2\\
\to \left[ \begin{array}{l}
x + 1 + x - 1 = 2\left( {DK:x \ge 1} \right)\\
x + 1 - x + 1 = 2\left( {DK:1 > x > - 1} \right)\\
- x - 1 - x + 1 = 2\left( {DK:x \le - 1} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = 2\\
2 = 2\left( {ld} \right)\\
- 2x = 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1\\
- 2x = 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1\\
x = - 1
\end{array} \right.\left( {TM} \right)
\end{array}\)
