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\(\frac{2}{5}x+\frac{3}{10}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.........+\frac{1}{9}-\frac{1}{10}\)
\(\frac{2}{5}x+\frac{3}{10}=1-\frac{1}{10}=\frac{9}{10}\)
\(\frac{2}{5}x=\frac{9}{10}-\frac{3}{10}=\frac{3}{5}\)
\(x=\frac{\frac{3}{5}}{\frac{2}{5}}=\frac{3}{2}\)
Ta có: \(\frac{1}{1x2}\)+ \(\frac{1}{2x3}\)+ \(\frac{1}{3x4}\)+ \(\frac{1}{4x5}\)+ .....+ \(\frac{1}{9x10}\)
= \(1-\left(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.....-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
= 1 - \(\frac{1}{10}\)
= \(\frac{9}{10}\)
a) I x+1/2 I = 4/9 : 2/3
I x+1/2 I = 2/3
\(\Rightarrow\orbr{\begin{cases}x+\frac{1}{2}=\frac{2}{3}\\x+\frac{1}{2}=-\frac{2}{3}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{6}\\x=-\frac{7}{6}\end{cases}}}\)
Bài b tương tự bạn nhé
a) \(\frac{2}{3}|x+\frac{1}{2}|=\frac{4}{9}\)
\(\Leftrightarrow|x+\frac{1}{2}|=\frac{2}{3}\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{2}=\frac{2}{3}\\x+\frac{1}{2}=-\frac{2}{3}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{6}\\x=-\frac{7}{6}\end{cases}}\)
b) \(\frac{3}{4}-|2x-\frac{4}{5}|=\frac{1}{2}\)
\(\Leftrightarrow|2x-\frac{4}{5}|=\frac{1}{4}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{4}{5}=\frac{1}{4}\\2x-\frac{4}{5}=-\frac{1}{4}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=\frac{21}{20}\\2x=\frac{11}{20}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{21}{40}\\x=\frac{11}{40}\end{cases}}\)
a, \(\frac{4x}{3}=\frac{14x}{3}+5\)
\(\frac{4x}{3}-\frac{14x}{3}=5\)
\(\frac{-10x}{3}=5\)
x=-1,5
b, 3x-5x=2-4
-2x=-2
x=1
c, \(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\right)\) .x=2
\(\left(\frac{1}{1}-\frac{1}{12}\right).x=2\)
\(\frac{11}{12}.x=2\)
x=\(\frac{24}{11}\)
d, \(x=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{101.103}\right)\)
\(x=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{101}-\frac{1}{103}\right)\)
x=\(\frac{1}{2}\left(1-\frac{1}{103}\right)\)
x=\(\frac{1}{2}.\frac{102}{103}\)
x=\(\frac{51}{103}\)
a) Ta có: \(\frac{x-2}{15}=\frac{9}{5}\Rightarrow5.\left(x-2\right)=9.15\)
\(\Rightarrow5x-10=135\)
\(\Rightarrow5x=145\)
\(\Rightarrow x=29\)
b) \(\frac{2-x}{16}=\frac{-4}{x-2}\Rightarrow\left(2-x\right).\left(x-2\right)=\left(-4\right).16\)
\(\Rightarrow4x-x^2-4=-64\)
\(\Rightarrow4x-x^2=-60\)
Lập bảng rồi tính ra
c) \(\frac{14}{x}=\frac{x-1}{4}\Rightarrow x.\left(x-1\right)=14.4\)
\(\Rightarrow x.\left(x-1\right)=56\)
Vì 56 = 8 x 7
\(\Rightarrow x=8\)
Câu c) còn có thêm \(x=-7\) nữa nha MMS_Hồ Khánh Châu vì \(x\inℤ\) mà :')
a) (x - 1/2) x 2 = 9/16
=> x - 1/2 = 9/16 : 2
=> x - 1/2 = 9/16 x 1/2
=> x - 1/2 =9/32
=> x = 9/32 + 1/2
=> x = 25/32
b) |x + 1/2| = 3/4
=> x + 1/2 = 3/4 hoặc x + 1/2 =-3/4
=>x = 3/4 - 1/2 hoặc x = -3/4 -1/2
=>x = 1/4 hoặc x = -5/4
Vậy .........