Question

Solve  

\[\left| 4 - x \right| + 1 < 3\] 

Answer 1

\[\text{ As }, \left| 4 - x \right| + 1 < 3\]
\[ \Rightarrow \left| 4 - x \right| < 3 - 1\]
\[ \Rightarrow \left| 4 - x \right| < 2\]
\[ \Rightarrow - 2 < 4 - x < 2 \left( \text{ As }, \left| x \right| < a \Rightarrow - a < x < a \right)\]
\[ \Rightarrow - 2 - 4 < - x < 2 - 4\]
\[ \Rightarrow - 6 < - x < - 2\]
\[ \Rightarrow 2 < x < 6\]
\[ \therefore x \in \left( 2, 6 \right)\]