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1/2x + 1/5 = 2/3x - 1/4
=> 1/2x - 2/3x = -1/4 - 1/5
=> -1/6x = -9/20
=> x = -9/20 : (-1/6)
=> x = 27/10
\(\frac{1}{2}x+\frac{1}{5}=\frac{2}{3}x-\frac{1}{4}\)
\(\frac{1}{2}x=\frac{2}{3}x-\frac{1}{4}-\frac{1}{5}\)
\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}\)
\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}-\frac{2x}{3}\)
\(-\frac{x}{6}=-\frac{9}{20}\)
\(6\left(-\frac{x}{6}\right)=6\left(-\frac{9}{20}\right)\)
\(-x=-\frac{27}{10}\)
\(\Rightarrow x=-\frac{27}{10}\)
Mình tính từng cái ra nha, từng cái sẽ ra được kết quả của phép tính:
\(1-\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\left(1-\dfrac{1}{5}\right)-\dfrac{1}{6}\)
\(=\left(\dfrac{5}{5}-\dfrac{1}{5}\right)-\dfrac{1}{6}\)
\(=\dfrac{4}{5}-\dfrac{1}{6}\)
\(=\dfrac{24}{30}-\dfrac{5}{30}\)
\(=\dfrac{19}{30}\)
\(a,\dfrac{3}{5}+\dfrac{3}{5\cdot9}+\dfrac{3}{9\cdot13}+....+\dfrac{3}{97\cdot101}\)
\(=\dfrac{3}{4}\cdot\left(\dfrac{4}{5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+....+\dfrac{4}{97\cdot101}\right)\)
\(=\dfrac{3}{4}\cdot\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+....+\dfrac{1}{97}-\dfrac{1}{101}\right)\)
\(=\dfrac{3}{4}\cdot\left(1-\dfrac{1}{101}\right)\)
\(=\dfrac{3}{4}\cdot\dfrac{100}{101}\)
\(=\dfrac{75}{101}\)
\(b,\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot\left(1+\dfrac{1}{4}\right)\cdot....\cdot\left(1+\dfrac{1}{99}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot....\cdot\dfrac{100}{99}\)
\(=\dfrac{100}{2}=50\)
Tính nhanh:
a) \(\dfrac{3}{5}+\dfrac{3}{5.9}+\dfrac{3}{9.13}+...+\dfrac{3}{97.101}\)
= \(\dfrac{3}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{101}\right)\)
= \(\dfrac{3}{4}\left(1-\dfrac{1}{101}\right)\)
= \(\dfrac{3}{4}\times\dfrac{100}{101}\)
= \(\dfrac{75}{101}\)
b) \(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)...\left(\dfrac{1}{98}+1\right)\left(\dfrac{1}{99}+1\right)\)
\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{99}{98}.\dfrac{100}{99}\)
\(=\dfrac{3.4.5...99.100}{2.3.4...98.99}\)
\(=\dfrac{100}{2}\)
\(=50\)
`@` `\text {Ans}`
`\downarrow`
`a)`
\(\left(\dfrac{7}{8}-\dfrac{3}{4}\right)\cdot1\dfrac{1}{3}-\dfrac{2}{3}\cdot0,5\)
`=`\(\dfrac{1}{8}\cdot\dfrac{4}{3}-\dfrac{1}{3}\)
`=`\(\dfrac{1}{6}-\dfrac{1}{3}=-\dfrac{1}{6}\)
`b)`
\(\left(2+\dfrac{5}{6}\right)\div1\dfrac{1}{5}+\left(-\dfrac{7}{12}\right)\)
`=`\(\dfrac{17}{6}\div1\dfrac{1}{5}-\dfrac{7}{12}\)
`=`\(\dfrac{85}{36}-\dfrac{7}{12}=\dfrac{16}{9}\)
`c)`
\(75\%-1\dfrac{1}{2}+0,5\div\dfrac{5}{12}\)
`=`\(-\dfrac{3}{4}+\dfrac{6}{5}=\dfrac{9}{20}\)
a) \(\left(\dfrac{7}{8}-\dfrac{3}{4}\right).1\dfrac{1}{3}-\dfrac{2}{3}.0,5\)
\(=\left(\dfrac{7}{8}-\dfrac{6}{8}\right).\dfrac{4}{3}-\dfrac{2}{3}.\dfrac{1}{2}\)
\(=\dfrac{1}{8}.\dfrac{4}{3}-\dfrac{2}{3}.\dfrac{1}{2}\)
\(=\dfrac{1}{6}-\dfrac{1}{3}\)
\(=\dfrac{-1}{6}\)
b) \(\left(2+\dfrac{5}{6}\right):1\dfrac{1}{5}+\dfrac{-7}{12}\)
\(=\left(\dfrac{12}{6}+\dfrac{5}{6}\right):\dfrac{6}{5}+\dfrac{-7}{12}\)
\(=\dfrac{17}{6}.\dfrac{5}{6}+\dfrac{-7}{12}\)
\(=\dfrac{85}{36}+\dfrac{-7}{12}\)
\(=\dfrac{16}{9}\)
c) \(75\%-1\dfrac{1}{2}+0,5:\dfrac{5}{12}\)
\(=\dfrac{3}{4}-\dfrac{3}{2}+\dfrac{1}{2}.\dfrac{12}{5}\)
\(=\dfrac{3}{4}-\dfrac{6}{4}+\dfrac{6}{5}\)
\(=\dfrac{-3}{4}+\dfrac{6}{5}\)
\(=\dfrac{9}{20}\)
a) Ta có: \(\left|-5\right|+\left|x-1\right|=\left|7\right|\)
\(\Leftrightarrow\left|x-1\right|+5=7\)
\(\Leftrightarrow\left|x-1\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
Vậy: \(x\in\left\{3;-1\right\}\)
b) Ta có: \(2\cdot\left|2x-4\right|-\left|-4\right|=\left|-50\right|\)
\(\Leftrightarrow4\cdot\left|x-2\right|-4=50\)
\(\Leftrightarrow4\cdot\left|x-2\right|=54\)
\(\Leftrightarrow\left|x-2\right|=\dfrac{27}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=\dfrac{27}{2}\\x-2=-\dfrac{27}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{31}{2}\left(loại\right)\\x=-\dfrac{23}{2}\left(loại\right)\end{matrix}\right.\)
Vậy: \(x\in\varnothing\)
a, | -5 | + | x-1 | = | 7 |
5 + | x - 1 | = 7
| x - 1 | = 2
TH1 x -1 = 2
x = 3
TH2 x -1 = -2
x= -1
a. 3.(-5)2+2.(-6)0-56:7
=3.25+2.1-8
=69
b) 564+(-724)+564+224
=564.2+(-724+224)
=1128+(-500)
=628
c) (-8).25.(-2).4.(-5).125
=(-8.125).(25.4).(-2.-5)
=-1000.100.10
=-1000000
c=-1/5-5/4^2:5/8
c=-1/5-25/16:5/8
c=-1/5-5/2
c=-27/10