\(x+3\frac{1}{2}=24\frac{1}{4}-x\)
\(\Leftrightarrow x+x=24\frac{1}{4}-3\frac{1}{2}\)
\(\Leftrightarrow2x=\frac{94}{4}-\frac{14}{4}\)
\(\Leftrightarrow2x=\frac{90}{4}=\frac{45}{2}\)
\(\Leftrightarrow x=\frac{45}{2}:2\)
\(\Leftrightarrow x=\frac{45}{4}\)