Bài 1:
a) \(4\dfrac{1}{3}:\dfrac{x}{4}=6:0,3\)
\(\Rightarrow\dfrac{13}{3}.\dfrac{4}{x}=20\)
\(\Rightarrow\dfrac{52}{3x}=20\)
\(\Rightarrow52=20.3x\)
\(\Rightarrow60x=52\)
\(\Rightarrow x=\dfrac{13}{15}\)
b) \(\left(2^3:2^4\right).2^{x+1}=64\)
\(\Rightarrow2^{3-4}.2^{x+1}=64\)
\(\Rightarrow2^{-1}.2^{x+1}=64\)
\(\Rightarrow2^{-1+x+1}=64\)
\(\Rightarrow2^x=64\)
\(\Rightarrow2^x=2^6\)
\(\Rightarrow x=6\)
c) \(\left(x-1\right)^5=-32\)
\(\Rightarrow\left(x-1\right)^5=\left(-2\right)^5\)
\(\Rightarrow x-1=-2\)
\(\Rightarrow x=-2+1=-1\)
d) \(|3-2x|-3=-3\)
\(\Rightarrow|3-2x|=-3+3=0\)
\(\Rightarrow3-2x=0\)
\(\Rightarrow2x=3\)
\(\Rightarrow x=\dfrac{3}{2}\)
e) \(|x+\dfrac{4}{5}|-\dfrac{1}{7}=0\)
\(\Rightarrow|x+\dfrac{4}{5}|=\dfrac{1}{7}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{4}{5}=\dfrac{1}{7}\\x+\dfrac{4}{5}=-\dfrac{1}{7}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}-\dfrac{4}{5}\\x=-\dfrac{1}{7}-\dfrac{4}{5}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{23}{35}\\x=-\dfrac{33}{35}\end{matrix}\right.\)
Bài 2:
Ta có:
\(2x=3y=6z\)
\(=\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{1}{6}}\)
\(=\dfrac{x+y+z}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}}\) ( Áp dụng tính chất dãy tỉ số bằng nhau )
\(=\dfrac{1830}{1}=1830\)
Với \(\left\{{}\begin{matrix}2x=1830\\3y=1830\\6z=1830\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=915\\y=610\\z=305\end{matrix}\right.\)
