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\(\left(x-1\right)⋮\left(x+5\right)\)
\(\Rightarrow\left[\left(x+5\right)-6\right]⋮\left(x+5\right)\) mà \(\left(x+5\right)⋮\left(x+5\right)\)
\(\Rightarrow6⋮\left(x+5\right)\)
\(\Rightarrow\left(x+5\right)\in\left\{1;2;3;6;-1;-2;-3;-6\right\}\)
\(\Rightarrow x\in\left\{6;7;8;11;4;3;2;-1\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(4x+\left|x-2\right|-15\left(x+2\right)=0\)
\(\Rightarrow4x+\left|x-2\right|-15x-30=0\)
\(\Rightarrow-11x+\left|x-2\right|=30\)
\(\Rightarrow\left[{}\begin{matrix}-11x+x-2=30\left(đk:x\ge2\right)\\-11x-x+2=30\left(đk:x< 2\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{32}{-11}\left(ktm\right)\\x=\dfrac{-14}{6}\left(tm\right)\end{matrix}\right.\)
\(\left|2x-10\right|+\left|3y-4\right|=0\)
\(\left\{{}\begin{matrix}\left|2x-10\right|\ge0\\\left|3y-4\right|\ge0\end{matrix}\right.\)
\(\Rightarrow\left|2x-10\right|+\left|3y-4\right|\ge0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left|2x-10\right|=0\Rightarrow2x=10\Rightarrow x=5\\\left|3y-4\right|=0\Rightarrow3y=4\Rightarrow y=\dfrac{4}{3}\end{matrix}\right.\)
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\(2\left(\frac{3}{4}x-1\right)-3y\left(1-\frac{3}{4}x\right)=0\)
\(\Leftrightarrow\)\(2\left(\frac{3}{4}x-1\right)+3y\left(\frac{3}{4}x-1\right)=0\)
\(\Leftrightarrow\)\(\left(\frac{3}{4}x-1\right)\left(2+3y\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\frac{3}{4}x-1=0\\2+3y=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{4}{3}\\y=-\frac{2}{3}\end{cases}}\)