1)
a) \(\dfrac{3}{8}\left|x\right|=\dfrac{1}{4}\)
\(\Rightarrow\left|x\right|=\dfrac{1}{4}:\dfrac{3}{8}\)
\(\Rightarrow\left|x\right|=\dfrac{2}{3}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{2}{3}\end{matrix}\right.\)
b) \(\dfrac{\sqrt{x-1}}{4}=\dfrac{3}{8}+\left(\dfrac{2023}{2024}\right)^0\left(dk:x\ge1\right)\)
\(\Rightarrow\dfrac{\sqrt{x-1}}{4}=\dfrac{3}{8}+1\)
\(\Rightarrow\dfrac{\sqrt{x-1}}{4}=\dfrac{11}{8}\)
\(\Rightarrow\sqrt{x-1}=\dfrac{11}{8}\cdot4\)
\(\Rightarrow\sqrt{x-1}=\dfrac{11}{2}\)
\(\Rightarrow\left(\sqrt{x-1}\right)^2=\left(\dfrac{11}{2}\right)^2\)
\(\Rightarrow x-1=\dfrac{121}{4}\)
\(\Rightarrow x=\dfrac{121}{4}+1\)
\(\Rightarrow x=\dfrac{125}{4}\left(tm\right)\)
2)
a) \(\dfrac{4}{7}:\left(-\dfrac{2}{11}+\dfrac{1}{3}\right)+\dfrac{4}{7}:\left(-\dfrac{5}{11}+\dfrac{2}{3}\right)\)
\(=\dfrac{4}{7}:\dfrac{5}{33}+\dfrac{4}{7}:\dfrac{7}{33}\)
\(=\dfrac{4}{7}\cdot\dfrac{33}{5}+\dfrac{4}{7}\cdot\dfrac{33}{7}\)
\(=\dfrac{4}{7}\cdot\left(\dfrac{33}{5}+\dfrac{33}{7}\right)\)
\(=\dfrac{4}{7}\cdot\dfrac{396}{35}\)
\(=\dfrac{1584}{245}\)
\(\text{#}Toru\)
