Question

1. -15 <1 – 4x <9, χεZ​

Answer 1

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

Given that

$\rm :\longmapsto\: - 15 < 1 - 4x < 9$

★ On Subtracting 1 from each term, we get

$\rm :\longmapsto\: - 15 - 1 < 1 - 4x - 1< 9 - 1$

$\rm :\longmapsto\: - 16 < - 4x < 8$

★ On dividing each term by - 4, we get

$\rm :\longmapsto\:4 > x > - 2$

$\bf\implies \: - 2 < x < 4$

$\rm :\longmapsto\:As \: x \: \in \: Z$

$\bf\implies \:x = \{ - 1, \: 0, \: 1, \: 2, \: 3 \}$

Additional information :-

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

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

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

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

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

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