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1.
a) \(\frac{11}{2}-\frac{2}{3}:\left|2x+-\frac{3}{2}\right|=3\)
\(-\frac{2}{3}:\left|2x+-\frac{3}{2}\right|=3-\frac{11}{2}\)
\(-\frac{2}{3}:\left|2x+-\frac{3}{2}\right|=-\frac{5}{2}\)
\(\left|2x+-\frac{3}{2}\right|=-\frac{2}{3}:\left(-\frac{5}{2}\right)\)
\(\left|2x+-\frac{3}{2}\right|=\frac{4}{15}\)
\(\Rightarrow\left|2x+-\frac{3}{2}\right|\in\text{{}\frac{4}{15};-\frac{4}{15}\)}
Nếu, \(2x+\left(-\frac{3}{2}\right)=\frac{4}{15}\)
\(2x=\frac{53}{30}\)
\(x=\frac{53}{60}\)
Nếu, \(2x+\left(-\frac{3}{2}\right)=-\frac{4}{15}\)
\(2x=\frac{37}{30}\)
\(x=\frac{37}{60}\)
Vậy \(x\in\text{{}\frac{53}{60};\frac{37}{60}\)}
b) \(\left|\frac{2}{7}x-\frac{1}{5}\right|-\left|-x+\frac{4}{9}\right|=0\)
\(\left|\frac{2}{7}x-\frac{1}{5}\right|=\left|-x+\frac{4}{9}\right|\)
\(\Rightarrow\left|\frac{2}{7}x-\frac{1}{5}\right|\in\text{{}-x+\frac{4}{9};-\left(x+\frac{4}{9}\right)\)}
Nếu, \(\frac{2}{7}x-\frac{1}{5}=-x+\frac{4}{9}\)
\(x=\frac{203}{405}\)
Nếu, \(\frac{2}{7}x-\frac{1}{5}=-\left(-x+\frac{4}{9}\right)\)
\(\frac{2}{7}x-\frac{1}{5}=x-\frac{4}{9}\)
\(\frac{2}{7}x-x=\frac{1}{5}-\frac{4}{9}\)
\(-\frac{5}{7}x=-\frac{11}{45}\)
\(x=\frac{77}{225}\)
Vậy \(x\in\text{{}\frac{203}{405};\frac{77}{225}\)}
1a) \(\frac{5}{1,2}=\frac{-2,5}{x}\)
\(\Leftrightarrow5x=-3\)
\(\Leftrightarrow x=\frac{-3}{5}\)
b) \(\frac{3,2+\left(-0,4\right)}{-x-3,6}=\frac{-0,75}{1,5}\)
\(\Leftrightarrow\frac{2,8}{-x-3,6}=\frac{-0,75}{1,5}\)
\(\Leftrightarrow4,2=0,75x+2,7\)
\(\Leftrightarrow0,75x=1,5\)
\(\Leftrightarrow x=2\)
2) \(\frac{1}{3}.\frac{5}{7}=\frac{2}{7}.\frac{5}{6}\)
Tỉ lệ thức lập được \(\frac{5}{21}=\frac{10}{42}\)
\(\left(\frac{5}{x+3}-2\right).4=7-\left(\frac{9}{x+3}+\frac{1}{2}\right).2\)
\(\Leftrightarrow\frac{20}{x+3}-8=7-\frac{18}{x+3}+1\)
\(\Leftrightarrow\frac{20}{x+3}-8=8-\frac{18}{x+3}\)
\(\Leftrightarrow\frac{20}{x+3}+\frac{18}{x+3}=8+8\)
\(\Leftrightarrow\frac{38}{x+3}=16\)
\(\Leftrightarrow x+3=2,375\)
\(\Leftrightarrow x=-0,625\)
\(\left(\frac{5}{x+3}-2\right).4=7-\left(\frac{9}{x+3}+\frac{1}{2}\right).2\)
\(\Leftrightarrow\frac{20}{x+3}-8=7-\left(\frac{18}{x+3}+1\right)\)
\(\Leftrightarrow\frac{20}{x+3}-8=7-\frac{18}{x+3}-1\)
\(\Leftrightarrow\frac{20}{x+3}+\frac{18}{x+3}=7-1+8\)
\(\Leftrightarrow\frac{38}{x+3}=14\)
\(\Leftrightarrow\left(x+3\right)14=38\)
\(\Leftrightarrow14x+42=38\)
\(\Leftrightarrow14x=-4\Leftrightarrow x=-\frac{4}{14}=-\frac{2}{7}\)
Vậy \(x=-\frac{2}{7}\)
a) Ta có: \(\hept{\begin{cases}\left|x+\frac{1}{2}\right|\ge0\\\left|2y-1\right|\ge0\end{cases}}\)
\(\Rightarrow\left|x+\frac{1}{2}\right|+\left|2y-1\right|+11\ge11\)
\(\Rightarrow A\ge11\)
\(\Rightarrow\)GTNN của A là 11 \(\Leftrightarrow\hept{\begin{cases}\left|x+\frac{1}{2}\right|=0\\\left|2y-1\right|=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=-\frac{1}{2}\\y=\frac{1}{2}\end{cases}}\)
Vậy ...
b) Ta có: \(\hept{\begin{cases}\left|x-1,2\right|\ge0\\\left|y+1\right|\ge0\end{cases}}\)
\(\Rightarrow\left|x-1,2\right|+\left|y+1\right|+1\ge1\)
\(\Rightarrow\frac{1}{\left|x-1,2\right|+\left|y+1\right|+1}\le1\)
\(\Rightarrow\frac{7}{\left|x-1,2\right|+\left|y+1\right|+1}\le7\)
\(\Rightarrow B\le7\)
\(\Rightarrow\)GTNN của B là 7 \(\Leftrightarrow\hept{\begin{cases}\left|x-1,2\right|=0\\\left|y+1\right|=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=1,2\\y=-1\end{cases}}\)
Vậy ...
#)Giải : (Bài này ez mak :v)
\(\frac{a+2}{a-2}=\frac{b+3}{b-3}\)
\(\Rightarrow\left(a+2\right)\left(b-3\right)=\left(a-2\right)\left(b+3\right)\)(bước này mk làm tắt đi nhé)
\(\Rightarrow3a=2b\)
\(\Rightarrow\frac{a}{2}=\frac{b}{3}\)
\(\Rightarrowđpcm\)
Ta có: \(\frac{a+2}{a-2}=\frac{b+3}{b-3}\)
=> \(\frac{\left(a-2\right)+4}{a-2}=\frac{\left(b-3\right)+6}{b-3}\)
=> \(1+\frac{4}{a-2}=1+\frac{6}{b-3}\)
=> \(\frac{4}{a-2}=\frac{6}{b-3}\)
=> \(4\left(b-3\right)=6\left(a-2\right)\)
=> \(4b-12=6a-12\)
=> \(4b=6a\)
=> \(2b=3a\)
=> \(\frac{b}{3}=\frac{a}{2}\)