Tìm x phân số
X + 2/5 = 7/3
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Ta có: \(5\dfrac{1}{5}< x\dfrac{4}{15}< 9\dfrac{4}{13}\)
\(\Leftrightarrow\dfrac{26}{5}< \dfrac{15x+4}{15}< \dfrac{131}{13}\)
\(\Leftrightarrow\dfrac{1014}{195}< \dfrac{13\left(15x+4\right)}{195}< \dfrac{1965}{195}\)
\(\Leftrightarrow1014< 195x+52< 1965\)
\(\Leftrightarrow\left\{{}\begin{matrix}195x>962\\195x< 2017\end{matrix}\right.\Leftrightarrow\dfrac{962}{195}< x< \dfrac{2017}{195}\)
\(\Leftrightarrow x\in\left\{5;6;7;8;9;10\right\}\)
`(x-2)/6 -(x-1)/3 < x/2`
`<=> (x-2)/6 -(2(x-1))/6 < (3x)/6`
`<=> x-2 - (2x-2) <3x`
`<=> x-2-2x+2<3x`
`<=> -x <3x`
`<=> -x-3x<0`
`<=> -4x<0`
`<=> x>0`
Ta có: \(\dfrac{x+2}{x-3}< 0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+2>0\\x-3< 0\end{matrix}\right.\Leftrightarrow-2< x< 3\)
Vậy: S={x|-2<x<3}
Từ \(\frac{x}{y}=\frac{4}{5}\Rightarrow x=\frac{4}{5}y\)
Thay vào: \(x\cdot y=5\)ta có: \(\frac{4}{5}y\cdot y=5\Rightarrow y^2=\frac{25}{4}=\left(\frac{5}{2}\right)^2\)mà y> 0 => \(y=\frac{5}{2}\)và \(x=\frac{4}{5}\cdot\frac{5}{2}=2\)
Vậy x=2 và y = 5/2.
1.
\(\left(\frac{3}{1\times3}+\frac{3}{3\times5}+\frac{3}{5\times7}+...+\frac{3}{97\times99}\right)-x:\frac{3}{2}=\frac{7}{3}\\
\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{97\times99}\right):\frac{3}{2}-x:\frac{3}{2}=\frac{7}{3}\\\left[\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)-x\right]:\frac{3}{2}=\frac{7}{3}\\
\left(1-\frac{1}{99}\right)-x=\frac{7}{3}\times\frac{3}{2}\\
\frac{98}{99}-x=\frac{7}{2}\\
x=\frac{98}{99}-\frac{7}{2}=\frac{-497}{198}\)
2.\(\frac{x}{y}=\frac{4}{3}\Rightarrow\hept{\begin{cases}x=4a\\y=3a\\x-y=4a-3a=a\end{cases}}\\ \left(x-y\right)^{2015}=5^{2015}\Rightarrow x-y=5\\ \Rightarrow a=5\Rightarrow\hept{\begin{cases}x=4\times5=20\\y=3\times5=15\end{cases}}\)
\(\dfrac{\dfrac{22}{15}}{11-x}\) + \(\dfrac{2}{3}\) = \(\dfrac{7}{5}\)
\(\dfrac{\dfrac{22}{15}}{11-x}\) = \(\dfrac{7}{5}\) - \(\dfrac{2}{3}\)
\(\dfrac{\dfrac{22}{15}}{11-x}\) = \(\dfrac{11}{15}\)
11 - \(x\) = \(\dfrac{22}{15}\) : \(\dfrac{11}{15}\)
11 - \(x\) = 2
\(x\) = 11 - 2
\(x\) = 9
x +2/5 = 7/3
x = 7/3 -2/5
x = 29/15