Question

3x+5<6x-4 linear ineqation​

Answer 1

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

↝ Given inequality is

$\rm :\longmapsto\:3x + 5 < 6x - 4$

Subtracting 6x from both sides, we get

$\rm :\longmapsto\:3x + 5 - 6x < 6x - 4 - 6x$

$\rm :\longmapsto\:5 - 3x < - 4$

Subtracting 5 from both sides, we get

$\rm :\longmapsto\:5 - 3x - 5 < - 4 - 5$

$\rm :\longmapsto\: - 3x < - 9$

Divided by- 3 both sides, we get

$\rm :\longmapsto\:x > 3$

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

$\bf\implies \:x \: \in \: (3, \: \infty )$

Additional Information :-

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

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

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

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

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

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