Đáp án:
$\begin{array}{l}
d)\left| {2x - 1} \right| + \left| {1 - 3x} \right| = 2x + 1\\
\Rightarrow \left| {2x - 1} \right| + \left| {3x - 1} \right| = 2x + 1\\
+ Khi:x \ge \dfrac{1}{2} \Rightarrow \left\{ \begin{array}{l}
\left| {2x - 1} \right| = 2x - 1\\
\left| {3x - 1} \right| = 3x - 1
\end{array} \right.\\
\Rightarrow 2x - 1 + 3x - 1 = 2x + 1\\
\Rightarrow 3x = 3\\
\Rightarrow x = 1\left( {tmdk} \right)\\
+ Khi:\dfrac{1}{3} \le x < \dfrac{1}{2} \Rightarrow \left\{ \begin{array}{l}
\left| {2x - 1} \right| = 1 - 2x\\
\left| {3x - 1} \right| = 3x - 1
\end{array} \right.\\
\Rightarrow 1 - 2x + 3x - 1 = 2x + 1\\
\Rightarrow x = - 1\left( {ktm} \right)\\
+ Khi:x < \dfrac{1}{3}\\
\Rightarrow 1 - 2x + 1 - 3x = 2x + 1\\
\Rightarrow x = \dfrac{1}{7}\left( {tm} \right)\\
Vậy\,x = 1\,hoặc:x = \dfrac{1}{7}\\
e)\left| {x + 1} \right| - \left| {2x + 3} \right| = - x + 2\\
+ Khi:x \ge - 1 \Rightarrow \left\{ \begin{array}{l}
\left| {x + 1} \right| = x + 1\\
\left| {2x + 3} \right| = 2x + 3
\end{array} \right.\\
\Rightarrow x + 1 - 2x - 3 = - x + 2\\
\Rightarrow - 2 = 2\left( {vo\,nghiem} \right)\\
+ Khi: - \dfrac{3}{2} \le x < - 1\\
\Rightarrow - x - 1 - 2x - 3 = - x + 2\\
\Rightarrow x = - 3\left( {ktm} \right)\\
+ Khi:x < - \dfrac{3}{2}\\
\Rightarrow - x - 1 - \left( { - 2x - 3} \right) = - x + 2\\
\Rightarrow - x - 1 + 2x + 3 = - x + 2\\
\Rightarrow 2x = 0\\
\Rightarrow x = 0\left( {ktm} \right)
\end{array}$
Vậy phương trình vô nghiệm
