Question

a) \(\left|x+\dfrac{1}{4}\right|-4=-2\)

b) \(-\dfrac{15}{12}x+\dfrac{3}{7}=\dfrac{6}{5}x-\dfrac{1}{2}\)

Answer 1

a) \(\left|x+\dfrac{1}{4}\right|-4=-2\)

\(\Rightarrow\left|x+\dfrac{1}{4}\right|=2\)

\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{4}=2\\x+\dfrac{1}{4}=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{4}\\x=\dfrac{-9}{4}\end{matrix}\right.\)

b) \(-\dfrac{15}{12}x+\dfrac{3}{7}=\dfrac{6}{5}x-\dfrac{1}{2}\)

\(\Rightarrow\dfrac{-49}{20}x=\dfrac{-13}{14}\)

\(\Rightarrow x=\dfrac{130}{343}\)