Here's how to solve for x:

\(0.53 = x - \frac{91}{6}\)

Add \(\frac{91}{6}\) to both sides.

\(0.53 + \frac{91}{6}= x - \frac{91}{6} + \frac{91}{6} \\~\\ 0.53 + \frac{91}{6}= x \\~\\ \frac{53}{100} + \frac{91}{6}= x \\~\\ \frac{4709}{300} = x \\~\\ 15.69\overline6 = x\)