a)|7/5x+2/3-|-|4/3x-1/4|=0
b)|5x|-3x=2
giúp mik với ạ
a)|7/5x+2/3-|-|4/3x-1/4|=0
b)|5x|-3x=2
giúp mik với ạ
Đáp án:
$\begin{array}{l}
a)\left| {\dfrac{7}{5}x + \dfrac{2}{3}} \right| – \left| {\dfrac{4}{3}x – \dfrac{1}{4}} \right| = 0\\
\Rightarrow \left| {\dfrac{7}{5}x + \dfrac{2}{3}} \right| = \left| {\dfrac{4}{3}x – \dfrac{1}{4}} \right|\\
\Rightarrow \left[ \begin{array}{l}
\dfrac{7}{5}x + \dfrac{2}{3} = \dfrac{4}{3}x – \dfrac{1}{4}\\
\dfrac{7}{5}x + \dfrac{2}{3} = – \dfrac{4}{3}x + \dfrac{1}{4}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
\dfrac{7}{5}x – \dfrac{4}{3}x = – \dfrac{1}{4} – \dfrac{2}{3}\\
\dfrac{7}{5}x + \dfrac{4}{3}x = \dfrac{1}{4} – \dfrac{2}{3}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
\dfrac{1}{{15}}x = – \dfrac{{11}}{{12}}\\
\dfrac{{41}}{{15}}x = \dfrac{{ – 5}}{{12}}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = \dfrac{{ – 55}}{4}\\
x = \dfrac{{ – 75}}{{492}}
\end{array} \right.\\
b)\left| {5x} \right| – 3x = 2\\
\Rightarrow \left| {5x} \right| = 3x + 2\left( {dkxd:x \ge – \dfrac{2}{3}} \right)\\
\Rightarrow \left[ \begin{array}{l}
5x = 3x + 2\\
5x = – 3x – 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
2x = 2\\
8x = – 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1\left( {tmdk} \right)\\
x = – \dfrac{1}{4}\left( {tmdk} \right)
\end{array} \right.
\end{array}$
Vậy x=1 hoặc x=-1/4