1/2-/5/4-2x/=1/3 2x-/x+1/=-1/2 /2x-1/-/x+1/3/=0

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1. Giải thích các bước giải:

   Ta có:

   \(\begin{array}{l}
   a,\\
   \dfrac{1}{2} – \left| {\dfrac{5}{4} – 2x} \right| = \dfrac{1}{3}\\
    \Leftrightarrow \left| {\dfrac{5}{4} – 2x} \right| = \dfrac{1}{2} – \dfrac{1}{3}\\
    \Leftrightarrow \left| {\dfrac{5}{4} – 2x} \right| = \dfrac{1}{6}\\
    \Leftrightarrow \left[ \begin{array}{l}
   \dfrac{5}{4} – 2x = \dfrac{1}{6}\\
   \dfrac{5}{4} – 2x =  – \dfrac{1}{6}
   \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
   2x = \dfrac{5}{4} – \dfrac{1}{6}\\
   2x = \dfrac{5}{4} + \dfrac{1}{6}
   \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
   2x = \dfrac{{13}}{{12}}\\
   2x = \dfrac{{17}}{{12}}
   \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
   x = \dfrac{{13}}{{24}}\\
   x = \dfrac{{17}}{{24}}
   \end{array} \right.\\
   b,\\
   2x – \left| {x + 1} \right| =  – \dfrac{1}{2}\\
    \Leftrightarrow \left| {x + 1} \right| = 2x + \dfrac{1}{2}\\
    \Leftrightarrow \left\{ \begin{array}{l}
   2x + \dfrac{1}{2} \ge 0\\
   \left[ \begin{array}{l}
   x + 1 = 2x + \dfrac{1}{2}\\
   x + 1 =  – 2x – \dfrac{1}{2}
   \end{array} \right.
   \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
   x \ge  – \dfrac{1}{4}\\
   \left[ \begin{array}{l}
   x = \dfrac{1}{2}\\
   x =  – \dfrac{1}{2}
   \end{array} \right.
   \end{array} \right. \Leftrightarrow x = \dfrac{1}{2}\\
   c,\\
   \left| {2x – 1} \right| – \left| {x + \dfrac{1}{3}} \right| = 0\\
    \Leftrightarrow \left| {2x – 1} \right| = \left| {x + \dfrac{1}{3}} \right|\\
    \Leftrightarrow \left[ \begin{array}{l}
   2x – 1 = x + \dfrac{1}{3}\\
   2x – 1 =  – x – \dfrac{1}{3}
   \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
   x = \dfrac{4}{3}\\
   x = \dfrac{2}{9}
   \end{array} \right.
   \end{array}\)

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