Toán Lớp 8: Tìm x: (|2,5-x|)/(|1,5-x|)=3/4
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Toán Lớp 8: Tìm x: (|2,5-x|)/(|1,5-x|)=3/4
Comments ( 2 )
\dfrac{{\left| {2,5 – x} \right|}}{{\left| {1,5 – x} \right|}} = \dfrac{3}{4}\\
\Leftrightarrow \left| {\dfrac{{2,5 – x}}{{1,5 – x}}} \right| = \dfrac{3}{4}\\
DKXD:1,5 – x \ne 0\\
\Leftrightarrow x \ne 1,5\\
\Leftrightarrow \left[ \begin{array}{l}
\dfrac{{2,5 – x}}{{1,5 – x}} = \dfrac{3}{4}\\
\dfrac{{2,5 – x}}{{1,5 – x}} = – \dfrac{3}{4}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
4\left( {2,5 – x} \right) = 3\left( {1,5 – x} \right)\\
4\left( {2,5 – x} \right) = – 3\left( {1,5 – x} \right)
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
10 – 4x = 4,5 – 3x\\
10 – 4x = – 4,5 + 3x
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
– 4x + 3x = 4,5 – 10\\
– 4x – 3x = – 4,5 – 10
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
– x = – 5,5\\
– 7x = – 14,5
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 5,5\\
x = \dfrac{{29}}{{14}}
\end{array} \right.\\
\Rightarrow S \in \{ 5,5;\,\,\dfrac{{29}}{{14}}\}
\end{array}\]