Câu 14:
a) \(4x-\dfrac{1}{3}=-\dfrac{7}{3}\)
\(\Rightarrow4x=-\dfrac{7}{3}+\dfrac{1}{3}\)
\(\Rightarrow4x=-\dfrac{6}{3}\)
\(\Rightarrow4x=-2\)
\(\Rightarrow x=-2:4\)
\(\Rightarrow x=-\dfrac{1}{2}\)
b) \(-\dfrac{1}{3}x+\dfrac{2}{3}=\dfrac{1}{2}\left(1-\dfrac{1}{4}\right)\)
\(\Rightarrow-\dfrac{1}{3}x+\dfrac{2}{3}=\dfrac{1}{2}\cdot\dfrac{3}{4}\)
\(\Rightarrow-\dfrac{1}{3}x+\dfrac{2}{3}=\dfrac{3}{8}\)
\(\Rightarrow-\dfrac{1}{3}x=\dfrac{3}{8}-\dfrac{2}{3}\)
\(\Rightarrow-\dfrac{1}{3}x=-\dfrac{7}{24}\)
\(\Rightarrow x=-\dfrac{7}{24}:-\dfrac{1}{3}\)
\(\Rightarrow x=\dfrac{7}{8}\)
c) \(x^2-\dfrac{4}{16}=\dfrac{5}{16}\)
\(\Rightarrow x^2=\dfrac{5}{16}+\dfrac{4}{16}\)
\(\Rightarrow x^2=\dfrac{9}{16}\)
\(\Rightarrow x^2=\left(\dfrac{3}{4}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=-\dfrac{3}{4}\end{matrix}\right.\)
4:
a: \(\left(x-\dfrac{3}{5}\right):\dfrac{-1}{3}=0,4\)
=>\(x-\dfrac{3}{5}=\dfrac{2}{5}\cdot\dfrac{-1}{3}=\dfrac{-2}{15}\)
=>\(x=-\dfrac{2}{15}+\dfrac{3}{5}=\dfrac{-2}{15}+\dfrac{9}{15}=\dfrac{7}{15}\)
b: \(\left(x-1\right)^5=32\)
=>\(\left(x-1\right)^5=2^5\)
=>x-1=2
=>x=3
Câu 13:
a: \(-\dfrac{3}{5}-\left(\dfrac{5}{2}-\dfrac{3}{5}\right)\)
\(=-\dfrac{3}{5}-\dfrac{5}{2}+\dfrac{3}{5}\)
\(=-\dfrac{5}{2}\)
b: \(\dfrac{7}{3}\left(\dfrac{7}{15}-\dfrac{4}{9}\right)+\dfrac{7}{3}\left(\dfrac{8}{15}-\dfrac{5}{9}\right)\)
\(=\dfrac{7}{3}\left(\dfrac{7}{15}-\dfrac{4}{9}+\dfrac{8}{15}-\dfrac{5}{9}\right)\)
\(=\dfrac{7}{3}\left(1-1\right)=\dfrac{7}{3}\cdot0=0\)
c: \(S=2^2+4^2+...+22^2\)
\(=2^2\left(1^2+2^2+...+11^2\right)\)
\(=4\cdot506=2024\)
