Find all solutions x of the inequality

\(\frac{5}{24}+|x-\frac{11}{48}|<\frac{5}{16}\)

1) Isolate the absolute value part
\(|x-\frac{11}{48}|<\frac{5}{48}\)

2) For absolute value inequalities, split the inequality into two parts, then solve.

For one of the parts, just drop the absolute value and solve.
For the second part, drop the absolute value, flip the inequality sign and make the other side negative. 
\(x-\frac{11}{48}<\frac{5}{48}\\ x<\frac{16}{48}\\ x<\frac{1}{3}\) and  \(x-\frac{11}{48}>-\frac{5}{48}\\ x>\frac{6}{48}\\ x>\frac{1}{8}\)
3) Turn that into interval notation.

(1/8)

\((\frac{1}{8},\frac{1}{3})\)