Question

\(3\dfrac{1}{2}-\dfrac{1}{2}x=\dfrac{2}{3}\)

Answer 1

\(3\dfrac{1}{2}-\dfrac{1}{2}x=\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{7}{2}-\dfrac{1}{2}x=\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{1}{2}x=\dfrac{7}{2}-\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{1}{2}x=\dfrac{17}{6}\)

\(\Leftrightarrow x=\dfrac{17}{6}:\dfrac{1}{2}\)

\(\Leftrightarrow x=\dfrac{17}{3}\)

Answer 2

\(3\dfrac{1}{2}-\dfrac{1}{2}x=\dfrac{2}{3}\)

\(\Rightarrow\dfrac{7}{2}-\dfrac{1}{2}x=\dfrac{2}{3}\)

\(\Rightarrow7\cdot\dfrac{1}{2}-\dfrac{1}{2}x=\dfrac{2}{3}\)

\(\dfrac{1}{2}\left(7-x\right)=\dfrac{2}{3}\)

\(\Rightarrow7-x=\dfrac{2}{3}:\dfrac{1}{2}\)

\(\Rightarrow7-x=\dfrac{2}{3}\cdot\dfrac{2}{1}\)

\(\Rightarrow7-x=\dfrac{4}{3}\)

\(\Rightarrow x=7-\dfrac{4}{3}\)

\(\Rightarrow x=\dfrac{17}{3}\)