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\(\Rightarrow\left(x-3\right).\left(-11\right)=\left(5-2x\right).5\)
\(\Rightarrow-11x+33=25-10x\)
\(\Rightarrow-11x-10x+33=25\)
\(\Rightarrow-21x=25-33\)
\(\Rightarrow-21x=-8\)
\(\Rightarrow x=\frac{8}{21}\)
\(\frac{x-3}{5}=\frac{5-2x}{-11}\)
\(\Leftrightarrow-11\left(x-3\right)=5\left(5-2x\right)\)
\(\Leftrightarrow33-11x=25-10x\)
\(\Leftrightarrow-11x+10x=25-33\)
\(\Leftrightarrow-x=-8\Leftrightarrow x=8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
5 ( x - 11 ) = 2 ( 2x - 3 )
5x - 55 = 4x - 6
5x - 4x = -6 + 55
x = 49
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\(\frac{x-3}{5}=\frac{5-2x}{-11}\)
\(-11\cdot\left(x-3\right)=5\cdot\left(5-2x\right)\)
\(-11x+33=25-10x\)
\(-11x+33-25+10x=0\)
\(8-x=0\)
\(x=8\)
\(\left(x-3\right)\cdot\left(-11\right)=5\cdot\left(5-2x\right)\)
\(-11x+33=25-10x\)
\(-11x+33+10x=25\)
\(-x+33=25\)
\(x=-8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4x+11}{2x-5}=\frac{4x-10+21}{2x-5}=\frac{2\left(2x-5\right)}{2x-5}+\frac{21}{2x-5}=2+\frac{21}{2x-5}\)
Để \(\frac{4x+11}{2x-5}\in Z\Leftrightarrow\frac{21}{2x-5}\in Z\)\(\Rightarrow2x-5\inƯ_{21}\)
Mà \(Ư_{21}=\left\{\pm1;\pm3;\pm7\right\}\)
TH1 : \(2x-5=1\Rightarrow2x=6\Rightarrow x=3\)
TH2 : \(2x-5=-1\Rightarrow2x=4\Rightarrow x=2\)
TH3 : \(2x-5=3\Rightarrow2x=8\Rightarrow x=4\)
TH4 : \(2x-5=-3\Rightarrow2x=2\Rightarrow x=1\)
TH5 : \(2x-5=7\Rightarrow2x=12\Rightarrow x=6\)
TH6 : \(2x-5=-7\Rightarrow2x=-2\Rightarrow x=-1\)
\(KL:x\in\left\{-1;1;2;3;4;6\right\}\)
Để \(\frac{4x+11}{2x-5}\)là số nguyên
\(=\frac{4x-10+21}{2x-5}\)
\(=\frac{2\left(2x-5\right)}{2x-5}+\frac{21}{2x-5}\)
\(=2+\frac{21}{2x-5}\)
Để \(\frac{4x+11}{2x-5}\in Z\)
\(\Leftrightarrow\frac{21}{2x-5}\in Z\)
\(\Rightarrow2x-5\inƯ\left(21\right)\)
Ư(21)={1;-1;3;-3;-7;7}
Ta lập bảng
2x-5 | 1 | -1 | -3 | 3 | -7 | 7 |
x | 3 | 2 | 1 | 4 | -1 | 6 |
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(2x-3=\frac{1}{2}\Leftrightarrow2x=\frac{1}{2}+3\Leftrightarrow2x=\frac{7}{2}\Leftrightarrow x=\frac{7}{2}\div2\Leftrightarrow x=\frac{7}{4}\)
b)\(\frac{5}{12}x=\frac{-4}{15}\Leftrightarrow x=\frac{-4}{15}\div\frac{5}{12}\Leftrightarrow x=\frac{-6}{25}\)
c)\(2,7:2x=\frac{11}{5}:\frac{11}{3}\Leftrightarrow2,7:2x=\frac{3}{5}\Leftrightarrow2x=2,7:\frac{3}{5}\Leftrightarrow2x=4,5\Leftrightarrow x=4,5:2\Leftrightarrow x=2.25\)
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#)Giải :
\(\frac{2x+5}{2x-11}=\frac{2x-11+16}{2x-11}=\frac{2x-11}{2x-11}+\frac{16}{2x-11}=1+\frac{16}{2x-11}\)
Lập bảng xét Ư(16)
TL
\(\frac{2x+5}{2x-11}=\frac{2x-11+16}{2x-11}\)
\(=1+\frac{16}{2x-11}\)