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

Question

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

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1 year 2020-11-28T12:23:39+00:00 1 Answers 84 views 0

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