\(\left|3x-1\right|=\left|5x-2\right|\)

\(\Leftrightarrow\orbr{\begin{cases}3x-1=5x-2\\3x-1=2-5x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x=1\\8x=3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{3}{8}\end{cases}}\)

LÀ ĐÁP ÁN A

Đáp án A

\(\frac{1}{3}.3^4.3^x=3^7\)

\(3^4.3^x=3^7.3\)

\(3^4.3^x=3^8\)

\(3^x=3^8:3^4\)

\(3^x=3^4\)

\(\Rightarrow x=4\)

\(\frac{x+2021}{10}+\frac{2022+x}{9}=\frac{2023+x}{8}+\frac{2024+x}{7}\)

\(\frac{x+2021}{10}+1+\frac{x+2022}{9}+1=\frac{2023+x}{8}+1+\frac{2024+x}{7}+1\)

\(\frac{x+2031}{10}+\frac{x+2031}{9}=\frac{2031+x}{8}+\frac{2031+x}{7}\)

\(\Rightarrow\frac{x+2031}{10}+\frac{x+2031}{9}-\frac{x+2031}{8}-\frac{x+2031}{7}=0\)

\(\left(x+2031\right)\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\right)=0\)

\(\Rightarrow x+2031=0\)

\(x=-2031\)

\(2^x=2^4\)

\(\Rightarrow x\in\left\{-4;4\right\}\)

x=4 hoặc x= -4

\(\left|x+\frac{1}{3}\right|-\frac{2}{7}=\frac{5}{7}\)

\(\left|x+\frac{1}{3}\right|=\frac{5}{7}+\frac{2}{7}=1\)

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

\(\left|x+\frac{1}{3}\right|-\frac{2}{7}=\frac{5}{7}\) 

\(\Rightarrow\left|x+\frac{1}{3}\right|=1\)

\(\Leftrightarrow x+\frac{1}{3}=1\)hoặc      \(x+\frac{1}{3}=-1\) 

    \(\Rightarrow x=\frac{2}{3}\)        hoặc     \(x=\frac{-4}{3}\)

\(4,\left(378\right)=4+0,\left(378\right)=4+\frac{378}{999}=4+\frac{14}{37}=\frac{518+14}{37}=\frac{532}{37}\)

help me!