1)\(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\frac{x+1}{6}\)

\(\Leftrightarrow\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}-\frac{x+1}{5}-\frac{x+1}{6}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)

\(\Leftrightarrow\left(x+1\right)=0\).Do \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\ne0\)

\(\Leftrightarrow x=-1\)

\(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\frac{x+1}{6}\\ \Leftrightarrow\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}-\frac{x+1}{5}-\frac{x+1}{6}=0\\ \Leftrightarrow\left(x+1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)

Gọi \(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)\)là A

Vì A ≠0

⇒\(x+1=0\Rightarrow x=-1\)

Vậy \(x=-1\)

\(0,81:\frac{x}{2}=\frac{16}{x^4}:\left(-0.9\right)\)

=> \(\frac{81}{100}:\frac{x}{2}=\frac{16}{x^4}:\frac{-9}{10}\)

=> \(\frac{81}{50x}=\frac{160}{-9.x^4}\)

=> \(81.\left(-9\right)x^4=50x.160\)

=> \(-729.x^4=8000.x\)

=> \(x^4:x=8000:\left(-729\right)\)

=> \(x^3=\frac{-8000}{729}\)

=> \(x^3=\frac{-20^3}{9^3}\)

=> \(x^3=\frac{-20}{9}^3\)

=> \(x=\frac{-20}{9}\)

thank you bạn xyz nha

a: \(\Leftrightarrow\left|x+2\right|=6x+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{1}{6}\\\left(6x+1-x-2\right)\left(6x+1+x+2\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{1}{6}\\\left(5x-1\right)\left(7x+3\right)=0\end{matrix}\right.\)

\(\Leftrightarrow x=\dfrac{1}{5}\)

b: Trường hợp 1: x<2

Pt sẽ là 3-x+2-x=7

=>5-2x=7

=>2x=-2

hay x=-1(nhận)

Trường hợp 2: 2<=x<3

Pt sẽ là 3-x+x-2=7

=>1=7(vô lý)

Trường hợp 3: x>=3

Pt sẽ là x-3+x-2=7

=>2x-5=7

=>x=6(nhận)

d: \(\Leftrightarrow4^x\cdot\left(1+4^3\right)=4160\)

\(\Leftrightarrow4^x=64\)

hay x=3

a ) \(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)

     \(\left(\frac{2}{5}-x\right):\frac{4}{3}+\frac{1}{2}=-4\)

     \(\left(\frac{2}{5}-x\right):\frac{4}{3}=-4-\frac{1}{2}\)

     \(\left(\frac{2}{5}-x\right):\frac{4}{3}=-\frac{9}{2}\)

        \(\frac{2}{5}-x=-\frac{9}{2}.\frac{4}{3}\)

        \(\frac{2}{5}-x=-3\)

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

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

                   \(x=\frac{3}{5}-\frac{15}{5}\)

                   \(x=-\frac{12}{5}\)

Vay \(x=-\frac{12}{5}\) 

b ) \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\left(1+\frac{2}{5}+\frac{2}{3}\right)=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\left(\frac{15}{15}+\frac{6}{15}+\frac{10}{15}\right)=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\left(\frac{15+6+10}{15}\right)=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\frac{31}{15}=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right)=-\frac{5}{4}.\frac{31}{15}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right)=-\frac{1}{4}.\frac{31}{3}\)

        \(-3+\frac{3}{x}-\frac{1}{3}=-\frac{31}{12}\)

        \(-3+\frac{3}{x}=-\frac{31}{12}+\frac{1}{2}\)

        \(-3+\frac{3}{x}=-\frac{31}{12}+\frac{6}{12}\)

        \(-3+\frac{3}{x}=\frac{-25}{12}\)

                     \(\frac{3}{x}=\frac{-25}{12}+3\)

                      \(\frac{3}{x}=\frac{-25}{12}+\frac{36}{12}\)

                      \(\frac{3}{x}=\frac{5}{6}\)

                      \(\frac{18}{6x}=\frac{5x}{6x}\)

Đèn dây , bạn tự làm tiếp nhé , de rồi chứ

a) \(\frac{1}{4}+\frac{1}{3}:2x=-5\)

\(\frac{1}{3}:2x=\frac{-21}{4}\)

\(2x=\frac{-4}{63}\)

\(x=\frac{2}{63}\)

b) \(\left(3x-\frac{1}{4}\right)\left(x+\frac{1}{2}\right)=0\)

\(\Rightarrow\orbr{\begin{cases}3x-\frac{1}{4}=0\\x+\frac{1}{2}=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{12}\\x=\frac{-1}{2}\end{cases}}\)

Vậy.........

c) \(\left|x+\frac{1}{5}\right|-\frac{1}{2}=\frac{9}{10}\)

\(\left|x+\frac{1}{5}\right|=\frac{7}{5}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{1}{5}=\frac{7}{5}\\x+\frac{1}{5}=\frac{-7}{5}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{6}{5}\\x=\frac{-8}{5}\end{cases}}\)

Vậy.........

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)

\(4x+\frac{15}{16}=\frac{23}{16}\)

\(4x=\frac{1}{2}\)

\(x=\frac{1}{8}\)

             Vậy \(x=\frac{1}{8}\)

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Rightarrow\left(x+x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Rightarrow5x+\frac{15}{32}=\frac{23}{16}\)

\(\Rightarrow5x=\frac{23}{16}-\frac{15}{32}\)

\(\Rightarrow5x=\frac{31}{32}\)

\(\Rightarrow x=\frac{31}{32}.\frac{1}{5}=\frac{31}{160}\)

Có 4x thôi Nguyễn Quang Trung

truoc tien quy dong roi tinh hoac so sanh voi 1/2 kich nhe

câu này ở trong Violympic nên mình nói luôn đáp án là 1/8