\(a)\frac{2}{3}x-\frac{1}{2}=\frac{5}{12}\)

\(\Rightarrow\frac{2}{3}x=\frac{5}{12}+\frac{1}{2}=\frac{11}{12}\)

\(\Rightarrow x=\frac{11}{12}:\frac{2}{3}=\frac{11}{8}\)

\(b)\left(2\frac{4}{5}x-50\right):\frac{2}{3}=51\)

\(\Rightarrow\frac{14}{5}x-50=51.\frac{2}{3}=34\)

\(\Rightarrow\frac{14}{5}x=34+50=84\)

\(\Rightarrow x=84:\frac{14}{5}=30\)

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) \(\left(2\frac{4}{5}.x-50\right):\frac{2}{3}=51\)

                  \(\frac{14}{5}.x-50=51.\frac{2}{3}\)

                   \(\frac{14}{5}.x-50=34\)

                                \(\frac{14}{5}.x=34+50\)

                                \(\frac{14}{5}.x=84\)

                                         \(x=84:\frac{14}{5}\)

                                         \(x=30\)

\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{11^2}>\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}\)

mà \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{2}-\frac{1}{12}=\frac{5}{12}\)

=>\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{11^2}>\frac{5}{12}\)

a)\(-\frac{2}{5}+\frac{2}{3}x+\frac{1}{6}x=-\frac{4}{5}\Leftrightarrow\frac{5}{6}x=-\frac{2}{5}\Leftrightarrow x=-\frac{12}{25}\)
Vậy nghiệm là x = -12/25

b)\(\frac{3}{2}x-\frac{2}{5}-\frac{2}{3}x=-\frac{4}{15}\Leftrightarrow\frac{5}{6}x=\frac{2}{15}\Leftrightarrow x=\frac{4}{25}\)
Vậy nghiệm là x = 4/25

c)\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
\(\Leftrightarrow x+1=0\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\right)\)\(\Leftrightarrow x=-1\)
Vậy nghiệm là x = -1
 

Cảm ơn bạnh nha. Chúc bạn buổi tối ấm =)))) <3

a) =-5/7 +7/8-2/7+1/8- -1/12+ -13/12

=(-5/7-2/7)+(7/8+1/8)-(-1/12--13/12)

=-7/7+8/8 - 12/12

= -1+1+1

=1

b)= ( -3/8+11/8)-(12/11+ -1/11)+(-3/5- 2/5)

= 1- 1 + (-1)

=-1

dễ lắm ó

\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)

\(\Leftrightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)

\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)\)

Dễ thấy: \(\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)\ne0\Rightarrow x+2004=0\Leftrightarrow x=-2014\)

x = -2014

ti-ck nha

.........

\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)

\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)\left(x+1\right)=0\)

\(\Rightarrow x+1=0\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\right)\)

\(x=-1\)

Vậy \(x=-1\)

\(B=\frac{1}{5}-\frac{3}{7}+\frac{5}{9}-\frac{2}{11}+\frac{7}{13}-\frac{9}{16}-\frac{7}{13}+\frac{2}{12}-\frac{5}{9}+\frac{3}{7}-\frac{1}{5}-\frac{1}{5}\)

\(B=\left(\frac{1}{5}-\frac{1}{5}\right)-\left(\frac{3}{7}-\frac{3}{7}\right)+\left(\frac{5}{9}-\frac{5}{9}\right)+\left(\frac{7}{13}-\frac{7}{13}\right)-\frac{2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)

\(B=0-0+0+0-\frac{2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)

\(B=\frac{-2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)

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