Question

25-4x< or equal to 16. find the smallest value of x when (i)x belongs to R (ii)x belongs to Z​

Answer 1

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

↝ Given inequality is

$\rm :\longmapsto\:25 - 4x \leqslant 16$

On Subtracting 25 from both sides, we get

$\rm :\longmapsto\:25 - 4x - 25 \leqslant 16 - 25$

$\rm :\longmapsto\: - 4x \leqslant - 9$

On dividing both sides by - 4, we get

$\bf\implies \:x \geqslant \dfrac{9}{4}$

$\: \: \: \: \: \: \: \: \: \: \green{ \boxed{ \because \: \bf \: - x \leqslant - y \: \implies \: x \geqslant y}}$

Case :- 1 When x belongs to R

$\red{\bf :\longmapsto\:x \: \in \: \bigg[\dfrac{9}{4} , \: \infty ) }$

Case :- 2 When x belongs to Z

$\red{\bf :\longmapsto\:x \: = \{3, \: 4, \: 5, \: 6, \: . \: . \: . \}}$

Additional Information :-

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

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

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

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

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

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

$\green{ \boxed{ \bf \: xy > 0 \implies \: x > 0, \: y > 0 \: \: or \: \: x < 0, \: y < 0}}$

$\green{ \boxed{ \bf \: xy < 0 \implies \: x > 0, \: y < 0 \: \: or \: \: x < 0, \: y > 0}}$