\(\left(\frac{5}{2.7}+\frac{5}{7.12}+\frac{5}{17.22}+\frac{5}{22.27}+\frac{5}{27.32}\right)x=945\)

\(\left(\frac{7-2}{2.7}+\frac{12-7}{7.12}+\frac{17-12}{12.17}+\frac{22-17}{17.22}+\frac{27-22}{22.27}+\frac{32-27}{27.32}\right)x=945\)

\(\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{27}-\frac{1}{32}\right)x=945\)

\(\left(\frac{1}{2}-\frac{1}{32}\right)x=945\Leftrightarrow\frac{15}{32}x=945\Leftrightarrow x=945:\frac{15}{32}=2016\)

A = 1 - \(\dfrac{5}{6}\)+\(\dfrac{7}{12}\)-\(\dfrac{9}{20}\)+\(\dfrac{11}{30}\)-\(\dfrac{13}{42}\)+\(\dfrac{15}{56}\) - \(\dfrac{17}{72}\)+\(\dfrac{19}{90}\)+\(\dfrac{23}{132}\)-\(\dfrac{25}{156}\)

A = 1 - \(\dfrac{5}{2.3}\)+\(\dfrac{7}{3.4}\)-\(\dfrac{9}{4.5}\)+\(\dfrac{11}{5.6}\)-\(\dfrac{13}{6.7}\)+\(\dfrac{15}{7.8}\)-\(\dfrac{17}{8.9}\)+\(\dfrac{19}{9.10}\)+\(\dfrac{23}{11.12}\)-\(\dfrac{25}{12.13}\)

A = 1 - \(\dfrac{1}{2}-\dfrac{1}{3}\)+\(\dfrac{1}{3}+\dfrac{1}{4}\)-\(\dfrac{1}{4}-\dfrac{1}{5}\)+...+\(\dfrac{1}{11}+\dfrac{1}{12}\)- \(\dfrac{1}{12}-\dfrac{1}{13}\)

A = 1 - \(\dfrac{1}{2}\) - \(\dfrac{1}{13}\) 

A = \(\dfrac{1}{2}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{11}{26}\) 

\(a,\left(x-5\right).\frac{30}{100}=\frac{200x}{100}+5\)

\(\left(x-5\right).\frac{3}{10}=2x+5\)

\(\frac{3x}{10}-\frac{3}{2}=2x+5\)

\(\frac{3}{10}x-2x=\frac{3}{2}+5\)

\(x\left(\frac{3}{10}-2\right)=\frac{13}{2}\)

\(x.\frac{-17}{10}=\frac{13}{2}\)

\(x=\frac{13}{2}:\frac{-17}{10}\)

\(x=\frac{13}{2}\cdot\frac{-10}{17}\)

\(x=\frac{-65}{17}\)

Vậy \(x=\frac{-65}{17}\)

Bài 2:

Ta có:\(\frac{-5x}{21}+\frac{-5y}{21}+\frac{-5z}{21}=\frac{-5}{21}\left(x+y+z\right)\)

Mà đề bài cho \(x+y=-z\Rightarrow\frac{-5}{21}\left(-z+z\right)=\frac{-5}{21}.0=0\Rightarrow A=0\)

Vậy \(A=0\)

1) -3-(-x) =5

=> -3 + x = 5

=> x = 5 - (-3)

=> x = 8

2)-9-(x-3)=12

=> x- 3 = (-9) - 12

=> x-3 =-21

=> x = (-21)+3

=> x = -18

3)-10-(x-5)=-5

x-5 = (-10) -(-5)

x-5 = -5

x = -5 +5

x = 0

4)210-(10-x) =110

10-x = 210 -110

10-x = 100

x = 10 -100

x = -90

5)4x-(2x-5)=21

=> 4x-2x + 5 =21

=> x(4-2) + 5 = 21

=> x.2 =21 - 5

=> x.2 = 16

=> x = 16:2

=> x = 8

6)14x-5=8x+10

7)15+5x =3x+30

8)2x-5=15-3x

9)2(3x+5)+3(x+1)=x+220

10)4.(x-2+5(x-3)=18

tên j đấy

a, \(\frac{5}{11.16}+\frac{5}{11.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

=\(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

=\(\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

a, A=1/11-1/16+1/16-1/21+1/21-1/26+...+1/61-1/66

      = 1/11-1/66=5/66 ( A chính là biểu thức ở phần a)

b, 1/12+1/20+1/30+...+1/110

=1/3.4+1/4.5+1/5.6+..+1/10.11

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11

=1/3-1/11=8/33

\(A=\frac{3}{2}-\frac{5}{6}+\frac{13}{12}-\frac{19}{20}+\frac{31}{30}-\frac{41}{42}+\frac{57}{56}-\frac{71}{72}+\frac{91}{90}-\frac{109}{110}\)

\(\Rightarrow A=\left(1+\frac{1}{2}\right)-\left(1-\frac{1}{6}\right)+\cdot\cdot\cdot+\left(1+\frac{1}{90}\right)-\left(1-\frac{1}{110}\right)\)

\(\Rightarrow A=1+\frac{1}{2}-1+\frac{1}{6}+\cdot\cdot\cdot+1+\frac{1}{90}-1+\frac{1}{110}\)

\(\Rightarrow A=\left[\left(1-1\right)+\frac{1}{2}+\frac{1}{6}\right]+\cdot\cdot\cdot+\left[\left(1-1\right)+\frac{1}{90}+\frac{1}{110}\right]\)

\(\Rightarrow A=\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{90}+\frac{1}{110}\)

\(\Rightarrow A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdot\cdot\cdot+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\cdot\cdot\cdot+\frac{1}{10}-\frac{1}{11}\)

\(\Rightarrow A=1-\frac{1}{11}\)

\(\Rightarrow A=\frac{10}{11}\)

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