Đáp án+Giải thích các bước giải:
$a.\\3x -|x-1| =0\\\Leftrightarrow\left[ \begin{array}{l}3x -(x-1)=0, x-1\ge 0\\\\3x -[-(x-1)]=0, x-1<0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}2x +1 =0, x\ge 1\\\\4x-1=0, x <1\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=-\dfrac{1}{2}, x \ge 1\\\\x=\dfrac{1}{4}, x < 1\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x\in \emptyset \\\\x=\dfrac{1}{4}\end{array} \right.\\b.\\|5-2x| -\dfrac{2}{3} x =1\\\Leftrightarrow 3\times |5x -2x|-2x=3\\\Leftrightarrow \left[ \begin{array}{l}3(5-2x)-2x = 3, 5-2x \ge 0\\\\3[-(5-2x)]-2x =3, 5-2x <0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}15 - 6x - 2x =3, x \le \dfrac{5}{2}\\\\-15 + 6x - 2x =3, x > \dfrac{5}{2}\end{array} \right. \\\Leftrightarrow \left[ \begin{array}{l}-8x =-12x \le \dfrac{5}{2}\\\\x>\dfrac{5}{2}\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{3}{2}, x\le \dfrac{5}{2}\\\\x=\dfrac{9}{2}, x>\dfrac{5}{2}\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{3}{2}\\\\x=\dfrac{9}{2}\end{array} \right.\\c.\\\dfrac{1}{2}x + |3x-2|=1\\\Leftrightarrow x+2\times |3x-2|=2 \\\Leftrightarrow \left[ \begin{array}{l}x+2(3x-2)=2, 3x-2 \ge 0\\\\x+2 [-(3x-2)] =2, 3x-2<0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}7x =6, x \ge \dfrac{2}{3}\\\\-5x =-2, x <\dfrac{2}{3}\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{6}{7}\\x=\dfrac{2}{5}\end{array} \right. $
