\(\dfrac{1}{2}x+2\dfrac{1}{2}=3\dfrac{1}{2}x-\dfrac{3}{4}\\ \Rightarrow\dfrac{1}{2}x+\dfrac{5}{2}=\dfrac{7}{2}x-\dfrac{3}{4}\\ \Rightarrow\dfrac{1}{2}x+\dfrac{5}{2}-\dfrac{7}{2}x+\dfrac{3}{4}=0\\ \Rightarrow-3x+\dfrac{13}{4}=0\\ \Rightarrow-3x=-\dfrac{13}{4}\\ \Rightarrow x=\dfrac{13}{12}\)
\(\dfrac{1}{2}x+2\dfrac{1}{2}=3\dfrac{1}{2}x-\dfrac{3}{4}\)
<=> \(\dfrac{x}{2}+\dfrac{5}{2}=\dfrac{7x}{2}-\dfrac{3}{4}\)
<=> \(\dfrac{2x}{4}+\dfrac{10}{4}=\dfrac{14x}{4}-\dfrac{3}{4}\)
<=> 2x + 10 = 14x - 3
<=> 10 + 3 = 14x - 2x
<=> 12x = 13
<=> \(\dfrac{13}{12}\)