Question

Please solve the problem, and don't give unnecessary answer.
Class 10 chapter Linear Inequation (ICSE)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given inequality is

$\rm :\longmapsto\:\dfrac{1}{2} \leqslant x + 1 - \dfrac{x - 2}{2} < 2\dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{1}{2} \leqslant \dfrac{2x + 2 - (x - 2)}{2} < \dfrac{5}{2}$

$\rm :\longmapsto\:\dfrac{1}{2} \leqslant \dfrac{2x + 2 - x + 2}{2} < \dfrac{5}{2}$

$\rm :\longmapsto\:\dfrac{1}{2} \leqslant \dfrac{x + 4}{2} < \dfrac{5}{2}$

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 :-

$\boxed{ \rm{ x > y\rm \implies\: - x < - y}}$

$\boxed{ \rm{ x < y\rm \implies\: - x > - y}}$

$\boxed{ \rm{ x < - y\rm \implies\: - x > y}}$

$\boxed{ \rm{ x > - y\rm \implies\: - x < y}}$

$\boxed{ \rm{ x \geqslant y\rm \implies\: - x \leqslant - y}}$

$\boxed{ \rm{ x \leqslant y\rm \implies\: - x \geqslant - y}}$

$\boxed{ \rm{ x \leqslant - y\rm \implies\: - x \geqslant y}}$