Question

Solve the inequality |2x+7|<27

Answer 1

|2x+7|<27 means that 2x+7 is less than 27 units from 0.

Answer 2

That means it must be between 27 and -27 so that is what you should write:
-27<2x+7<27
and solve that.

Answer 3

\(\large |2x+7|<27\implies
\begin{cases}
+(2x+7)<27\\ \quad \\
-(2x+7)<27
\end{cases}\)