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a)
\(\frac{2}{3}\div x-\frac{1}{2}=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}\div x=\frac{1}{3}+\frac{1}{2}\)
\(\Rightarrow\frac{2}{3}\div x=\frac{5}{6}\)
\(\Rightarrow x=\frac{2}{3}\div\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{5}\)
Vậy \(x=\frac{4}{5}\)
b)
\(\frac{3}{4}.x+\frac{2}{5}=\frac{5}{2}\)
\(\Rightarrow\frac{3}{4}.x=\frac{5}{2}-\frac{2}{5}\)
\(\Rightarrow\frac{3}{4}.x=\frac{21}{10}\)
\(\Rightarrow x=\frac{21}{10}\div\frac{3}{4}\)
\(\Rightarrow x=\frac{14}{5}\)
Vậy \(x=\frac{14}{5}\)
Các bước chi tiết mình không trình bày ra nha.
a) 2/3:x-1/2=1/3
2/3:x=1/3+1/2
2/3:x=5/6
x=2/3:5/6
x=4/5
b) 3/4.x+2/5=5/2
3/4.x=5/2-2/5
3/4.x=21/10
x=21/10:3/4
x=14/5
Bài 1 : \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right]:5\times x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{1}{24}+\frac{2}{15}+\frac{3}{40}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{5}{12}:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{1}{12}\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{x}{12}< \frac{5}{6}\)
=> \(\frac{8}{12}< \frac{x}{12}< \frac{10}{12}\)
=> x = 9
Bài 2 : \(\frac{\left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right]}{x}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
=> \(\frac{\left[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right]}{x}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{11\cdot12}\)
=> \(\frac{\left[1-\frac{1}{16}\right]}{x}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=1-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=\frac{11}{12}\)
=> \(\frac{15}{16}:x=\frac{11}{12}\)
=> \(x=\frac{45}{44}\)
Bài 3 : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\times(x+1):2}=\frac{399}{400}\)
=> \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\times(x+1)}=\frac{399}{400}\)
=> \(2\left[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(2\left[\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(\left[\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right]=\frac{399}{800}\)
=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
=> \(\frac{1}{x+1}=\frac{1}{800}\)
=> x = 799
Bài 2 :
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\) (*)
Ta có : \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}=\frac{8+4+2+1}{16}=\frac{15}{16}\) (1)
Lại có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(=1\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+...+\left(-\frac{1}{11}+\frac{1}{11}\right)-\frac{1}{12}\)
\(=1-\frac{1}{12}=\frac{11}{12}\) (2)
Thay (1) và (2) vào biểu thức (*) ta được :
\(\frac{15}{16}:x=\frac{11}{12}\)
\(\Leftrightarrow x=\frac{15}{16}:\frac{11}{12}\)
\(\Leftrightarrow x=\frac{45}{44}\)
Vậy : \(x=\frac{45}{44}\)
trả lời
tui trả lời rui mà
chúc bà học tốt
nhớ k tui nha
cám ơn các bn
1/1x2 + 1/2x3+ 1/3x4+....+1/2009x2010
= 1/1-1/2 + 1/2-1/3+ 1/3-1/4+...+1/2009-1/2010
= 1/1-1/2010
= 2009/2010
\(\frac{1}{1\cdot2}+\cdot\cdot\cdot+\frac{1}{2009\cdot2010}\)
\(=1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{2009}-\frac{1}{2010}\)
\(=1-\frac{1}{2010}\)
\(=\frac{2009}{2010}\)
a) Ta có :
\(\frac{7}{12}< \frac{x}{24}< \frac{2}{3}\)
\(\Rightarrow\frac{14}{24}< \frac{x}{24}< \frac{16}{24}\)
\(\Rightarrow14< x< 16\)
\(\Rightarrow x=15\)
Vậy x = 15
b) \(\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=195\)
\(\Rightarrow\left(x+x+x+...+x\right)+\left(1+4+7+...+28\right)=195\)
\(\Rightarrow10x+145=195\)
\(\Rightarrow10x=195-145\)
\(\Rightarrow10x=50\)
\(\Rightarrow x=50:10\)
\(\Rightarrow x=5\)
Vậy x = 5
c) \(\left(x+0,5\right)+\left(x+1,5\right)+\left(x+2,5\right)=33\)
\(\Rightarrow\left(x+x+x\right)+\left(0,5+1,5+2,5\right)=33\)
\(\Rightarrow3x+4,5=33\)
\(\Rightarrow3x=33-4,5\)
\(\Rightarrow3x=28,5\)
\(\Rightarrow x=28,5:3\)
\(\Rightarrow x=9,5\)
Vậy x = 9,5
_Chúc bạn học tốt_
a, \(\frac{7}{12}\)\(< \)\(\frac{x}{24}\)\(< \)\(\frac{2}{3}\)
\(\frac{14}{24}\)\(< \)\(\frac{x}{24}\)\(< \)\(\frac{16}{24}\)
Số lớn hơn 14 và nỏ hơn 16 là : 15
\(\Rightarrow\)Vậy \(x\)= 15