Please solve the problem, and don't give unnecessary answer. Class 10

1.	Please solve the problem, and don't give unnecessary answer. Class 10 chapter Linear Inequation (ICSE)
Answer» $\large\underline{\sf{Solution-}}$ GIVEN inequality is $\rm :\longmapsto\:\dfrac{1}{<klux>2</klux>} \leqslant x + 1 - \dfrac{x - 2}{2} < 2\dfrac{1}{2}$ $\rm :\longmapsto\:\dfrac{1}{2} \leqslant \dfrac{2x + 2 - (x - 2)}{2} < \dfrac{5}{2}$ $\rm :\longmapsto\:\dfrac{1}{2} \leqslant \dfrac{2x + 2 - x + 2}{2} < \dfrac{5}{2}$ $\rm :\longmapsto\:\dfrac{1}{2} \leqslant \dfrac{x + 4}{2} < \dfrac{5}{2}$ On MULTIPLY by 2, each term we get $\rm :\longmapsto\:1 \leqslant x + 4 < 5$ On Subtracting 4, from each term, we get $\rm :\longmapsto\:1 - 4 \leqslant x + 4 - 4 < 5 - 4$ $\rm :\longmapsto\: - 3\leqslant x < 1$ $\bf\implies \:x \: \in \: [ - 3, \: 1)$ ADDITIONAL Information :- $\boxed{ \rm{ x > y\rm \implies\: - x < - y}}$ $\boxed{ \rm{ x < y\rm \implies\: - x > - y}}$ $\boxed{ \rm{ x < - y\rm \implies\: - x > y}}$ $\boxed{ \rm{ x > - y\rm \implies\: - x < y}}$ $\boxed{ \rm{ x \geqslant y\rm \implies\: - x \leqslant - y}}$ $\boxed{ \rm{ x \leqslant y\rm \implies\: - x \geqslant - y}}$ $\boxed{ \rm{ x \leqslant - y\rm \implies\: - x \geqslant y}}$