Solve for $x$: $\;\;\;$ $\left|5 - 2x\right| < 1$
Given problem: $\;\;\;$ $\left|5 - 2x\right| < 1$ $\;\;\; \cdots \; (1)$
Now, $\;$ $\left|5 - 2x\right| = 5 - 2x$ $\;$ (when $\;$ $5 - 2x > 0$), $\;$ equation $(1)$ becomes
$5 - 2x < 1$
i.e. $\;$ $4 < 2x$ $\implies$ $2 < x$ $\;\;\; \cdots \; (2a)$
$\left|5 - 2x\right| = -\left(5 - 2x\right)$ $\;$ (when $\;$ $5 - 2x < 0$), $\;$ equation $(1)$ becomes
$-5 + 2x < 1$
i.e. $\;$ $2x < 6$ $\implies$ $x < 3$ $\;\;\; \cdots \; (2b)$
From $(2a)$ and $(2b)$, solution of inequation $(1)$ is $\;$ $2 < x < 3$