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1) Tìm x
\(\frac{11}{2}.x+\frac{1}{3}.x=1\)
\(\Rightarrow x\left(\frac{11}{2}+\frac{1}{3}\right)=1\)
\(\Rightarrow x\left(\frac{33}{6}+\frac{2}{6}\right)=1\)
\(\Rightarrow x.\frac{35}{6}=1\)
\(\Rightarrow x=\frac{6}{35}\)
2) So sánh
\(\frac{59}{40}< \frac{50}{31}\)( cái này bạn quy đồng là ra, mik chỉ ghi kq, bạn tự tính )
3)\(\frac{1}{3}+\frac{4}{7}-\frac{5}{14}-\frac{1}{2}-\frac{2}{3}\)
\(=\left(\frac{1}{3}-\frac{2}{3}\right)+\left(\frac{4}{7}-\frac{5}{14}\right)-\frac{1}{2}\)
\(=-\frac{1}{3}+\frac{3}{14}-\frac{1}{2}\)
\(=-\frac{13}{21}\)
1)\(\frac{11}{2}.x+\frac{1}{3}.x=1\)
\(x.\left(\frac{11}{2}+\frac{1}{3}=1\right)\)
\(x.\frac{35}{6}=1\)
\(x=1:\frac{35}{6}\)
\(x=\frac{6}{35}\)
2) Ta có:
\(\frac{59}{40}=\frac{1829}{1240}\)
\(\frac{50}{31}=\frac{2000}{1240}\)
Vì \(2000>1829\Rightarrow\frac{2000}{1240}>\frac{1829}{1240}\Rightarrow\frac{50}{31}>\frac{59}{40}\)
3)\(\frac{1}{3}+\frac{4}{7}-\frac{5}{14}-\frac{1}{2}-\frac{2}{3}\)
\(=\left(\frac{1}{3}-\frac{2}{3}\right)+\left(\frac{4}{7}-\frac{5}{14}-\frac{1}{2}\right)\)
\(=-\frac{1}{3}+\left(\frac{8}{14}-\frac{5}{14}-\frac{7}{14}\right)\)
\(=\frac{-1}{3}+\frac{-4}{14}\)
\(=\frac{-1}{3}+\frac{-2}{7}\)
\(=\frac{-7}{21}+\frac{-6}{21}\)
\(=\frac{-13}{21}\)
\(25\cdot\left(-\frac{1}{5}\right)^3+\frac{1}{5}-2\cdot\left(-\frac{1}{2}\right)^2-\frac{1}{2}\)
\(=25\cdot\left(-\frac{1}{125}\right)+\frac{1}{5}-2\cdot\frac{1}{4}-\frac{1}{2}\)
\(=-\frac{1}{5}+\frac{1}{5}-\frac{1}{2}-\frac{1}{2}\)
\(=0-\frac{1}{2}-\frac{1}{2}=-1\)
\(=25\cdot\frac{-1}{125}+\frac{1}{5}-2\cdot\frac{1}{4}-\frac{1}{2}\)
\(=-\frac{1}{5}+\frac{1}{5}-\frac{1}{2}-\frac{1}{2}\)
\(=-1\)
\(\frac{3}{2}+\frac{3}{14}+\frac{3}{15}+...+\frac{6}{\left(x-3\right).x}=\frac{96}{49}\)
\(\frac{6}{\left(1.2\right).2}+\frac{6}{\left(2.7\right).2}+...+\frac{6}{\left(x-3\right).x}=\frac{96}{49}\)
\(\frac{6}{1.4}+\frac{6}{4.7}+...+\frac{6}{\left(x-3\right).x}=\frac{96}{49}\)
\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{\left(x-3\right).x}=\frac{96}{49.2}\)
\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{\left(x-3\right)}-\frac{1}{x}=\frac{96}{98}\)
=> \(1-\frac{1}{x}=\frac{48}{49}\)
=> \(\frac{1}{x}=\frac{1}{49}\)
=> \(x=49\)
\(\Rightarrow2.\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{\left(2x-2\right).2x}\right)=\frac{1}{8}.2\).2
\(\Rightarrow\frac{2}{2.4}+\frac{2}{4.6}+...\frac{2}{\left(2x-2\right).2x}=\frac{1}{4}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2x-2}-\frac{1}{2x}=\frac{1}{4}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{2x}=\frac{1}{4}\)
\(\Rightarrow\frac{1}{2x}=\frac{1}{4}\Rightarrow\frac{1}{2x}=\frac{1}{2.2}\)
\(\Rightarrow x=2\)
\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x=0+\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)
\(\Leftrightarrow\frac{11}{15}x=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2}{5}\div\frac{11}{15}\)
\(\Leftrightarrow x=\frac{6}{11}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\times\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{50}{100}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{100}\)
\(\Leftrightarrow x+1=100\)
\(\Leftrightarrow x=100-1\)
\(\Leftrightarrow x=99\)
\(a)\frac{2}{3}x-\frac{1}{2}=\frac{5}{12}\)
\(\Rightarrow\frac{2}{3}x=\frac{5}{12}+\frac{1}{2}=\frac{11}{12}\)
\(\Rightarrow x=\frac{11}{12}:\frac{2}{3}=\frac{11}{8}\)
\(b)\left(2\frac{4}{5}x-50\right):\frac{2}{3}=51\)
\(\Rightarrow\frac{14}{5}x-50=51.\frac{2}{3}=34\)
\(\Rightarrow\frac{14}{5}x=34+50=84\)
\(\Rightarrow x=84:\frac{14}{5}=30\)
a) 2/3.x - 1/2 = 5/12
2/3.x = 5/12 + 1/2
2/3.x = 11/12
x = 11/12 : 2/3
x = 11/8
b) \(\left(2\frac{4}{5}.x-50\right):\frac{2}{3}=51\)
\(\frac{14}{5}.x-50=51.\frac{2}{3}\)
\(\frac{14}{5}.x-50=34\)
\(\frac{14}{5}.x=34+50\)
\(\frac{14}{5}.x=84\)
\(x=84:\frac{14}{5}\)
\(x=30\)
(2/3×x-1/3)=2/3+1/3
(2/3×x-1/3)=3/3
2/3×x=3/3+1/3
2/3×x=4/3
x=4/3:3/2
x=4/3×2/3
x=8/9
Cảm ơn mn lần nx ạ