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Bài 1:
a, \(\frac{1}{-16}-\frac{3}{45}=\frac{-1}{16}-\frac{1}{15}\)
\(=\frac{-15}{240}-\frac{16}{240}\)
\(=\frac{-31}{240}\)
b, \(=\frac{-10}{12}-\frac{-12}{12}\)
\(=\frac{2}{12}=\frac{1}{6}\)
c, \(=\frac{-30}{6}-\frac{1}{6}\)
\(=\frac{-31}{6}\)
Bài 2:
a, \(x=-\frac{1}{2}-\frac{3}{4}\)
\(x=-\frac{1}{4}\)
b, \(\frac{1}{2}+x=-\frac{11}{2}\)
\(x=-\frac{11}{2}-\frac{1}{2}\)
\(x=-6\)
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\(\frac{x-5}{3}=\frac{6}{5}\)
\(x-5=\frac{6}{5}.3\)
\(x-5=\frac{18}{5}\)
\(x=\frac{18}{5}+5\)
\(\Rightarrow x=\frac{43}{5}\)
Vậy ...
\(\frac{1}{3}=\frac{2-x}{4}\)
\(\frac{4}{3}=2-x\)
\(x=2-\frac{4}{3}\)
\(\Rightarrow x=\frac{2}{3}\)
Vậy ...
\(\frac{2}{3}x-\frac{3}{2}\left(x-\frac{1}{2}\right)=\frac{5}{12}\)
\(\Rightarrow\frac{2}{3}x-\frac{3}{2}x+\frac{3}{4}=\frac{5}{12}\)
\(\Rightarrow\frac{-5}{6}x=\frac{5}{12}-\frac{3}{4}=\frac{-1}{3}\)
\(\Rightarrow x=\frac{-1}{3}:\frac{-5}{6}=\frac{2}{5}\)
vậy x = \(\frac{2}{5}\)
= 2/3x - 3/2x - 3/2 × 1/2= 5/12
=> -5/6x - 3/4 = 5/12
=> -5/6x = 5/12 +3/4= 7/6
=>x=7/6 ÷ -5/6 =1/3
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b) \(\frac{4}{9}x-\frac{1}{2}=\frac{-5}{9}\)
\(\Rightarrow\frac{4}{9}x=\frac{-5}{9}+\frac{1}{2}\)
\(\Rightarrow\frac{4}{9}x=\frac{-1}{18}\)
\(\Rightarrow x=\frac{-1}{18}:\frac{4}{9}\)
\(\Rightarrow x=\frac{-1}{8}\)
\(\frac{1}{4}+\frac{1}{3}:\left(2x-1\right)=-5\)
\(\frac{1}{3}:\left(2x-1\right)=-5-\frac{1}{4}\)
\(\frac{1}{3}:\left(2x-1\right)=-\frac{20}{4}-\frac{1}{4}\)
\(\frac{1}{3}:\left(2x-1\right)=-\frac{21}{4}\)
\(\left(2x-1\right)=\frac{1}{3}:-\frac{21}{4}\)
\(\left(2x-1\right)=\frac{1}{3}.-\frac{4}{21}\)
\(\left(2x-1\right)=-\frac{4}{63}\)
2x= -4/63 + 1
2x = 59/63
x = 59/63 : 2
x = 59/126
1/3:(2.x-1)=-5-1/4
1/3:(2.x-1)=-21/4
2.x-1=1/3:-21/4
2.x-1=-4/63
2.x=-4/63+1
2.x=\(3\frac{59}{63}\)
x=\(3\frac{59}{63}\):2
x=\(1\frac{61}{63}\)
a) \(\frac{x}{4}=\frac{21}{28}\Rightarrow\frac{x}{4}=\frac{3}{4}\Rightarrow x=3\)
Vậy x = 3
b) \(\frac{2x}{5}=\frac{-24}{10}\Rightarrow\frac{2x}{5}=\frac{-12}{5}\Rightarrow2x=-12\Rightarrow x=-6\)
Vậy x = -6
\(a)\frac{x}{4}=\frac{21}{28}\)
\(\Rightarrow x\cdot28=4\cdot21\)
\(\Rightarrow x\cdot28=84\)
\(\Rightarrow x=3\)
\(b)\frac{2x}{5}=\frac{-24}{10}\)
Rút gọn : \(\frac{2x}{5}=\frac{-12}{5}\)
\(\Rightarrow2x=-12\)
\(\Rightarrow x=(-12)\div2=-6\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}=\frac{2001}{2003}\)
\(\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}\right)=\frac{1}{2}\cdot\frac{2001}{2003}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2001}{4006}\)
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left(x+1\right)}=\frac{2001}{4006}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{4006}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}\)
\(\frac{1}{x+1}=\frac{1}{2003}\)
\(\Rightarrow x+1=2003\)
\(x=2002\)
Vậy x = 2002
\(\frac{5}{x}=\frac{2y+1}{6}=x\left(2y+1\right)=5.6=30.\)vì y thuộc z nên 2y+1 thuộc z và x thuộc z mà x(2y+1)=30 nên x;2y+1 thuộc Ư(30)={-1;1;2;-2;3;-3;5;-5;6;-6;10;-10;15;-15;30;-30}.
Vì 2y+1 là số lẻ nên ta có bảng sau:
| x | 30 | -30 | 10 | -10 | 6 | -6 | 2 | -2 |
|---|---|---|---|---|---|---|---|---|
| 2y+1 | 1 | -1 | 3 | -3 | 5 | -5 | 15 | -15 |
| 2y | 0 | -2 | 2 | -4 | 4 | -6 | 14 | -16 |
| y | 0 | -1 | 1 | -2 | 2 | -3 | 7 | -8 |
Vậy các cặp số nguyên (x;y) thỏa mãn đề bài là:......................................
\(\frac{5}{3}x-\frac{2}{5}x=\frac{19}{10}\)
\(\left(\frac{5}{3}-\frac{2}{5}\right)x=\frac{19}{10}\)
\(\frac{19}{15}x=\frac{19}{10}\)
\(x=\frac{19}{30}\)
\(\frac{5}{3}x-\frac{2}{5}x=\frac{19}{10}\)
(5/3 - 2/5)x = 19/10
19/15x = 19/10
x = 19/30