Question

solve: -8½ < -½ - 4x < 7½, x=Z
​

Answer 1

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

$\rm :\longmapsto\: - 8\dfrac{1}{2} < - \dfrac{1}{2} - 4x < 7\dfrac{1}{2}$

$\rm :\longmapsto\: - \dfrac{17}{2} < - \dfrac{1}{2} - 4x < \dfrac{15}{2}$

$\red{\rm :\longmapsto\: \bf \: On \: adding \: \dfrac{1}{2} \: in \: each \: term}$

$\rm :\longmapsto\: \dfrac{1}{2} - \dfrac{17}{2} <\dfrac{1}{2} - \dfrac{1}{2} - 4x < \dfrac{15}{2} + \dfrac{1}{2}$

$\rm :\longmapsto\: \dfrac{1 - 17}{2} < - 4x < \dfrac{15 + 1}{2}$

$\rm :\longmapsto\: \dfrac{ - 16}{2} < - 4x < \dfrac{16}{2}$

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

$\red{\rm :\longmapsto\: \bf \: On \: dividing \:by \: - 4 \: each \: term}$

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

$\rm :\longmapsto\: - 2 < x < 2$

$\red{\bf :\longmapsto\:As \: it \: is \: given \: that \: x \: \in \: Z}$

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

Additional Information :-

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

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

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

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

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

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

$\boxed{ \green{ \tt \:\dfrac{x}{y} > 0 \implies \: x > 0, \: y > 0 \: \: or \: x < 0, \: y < 0 }}$

$\boxed{ \green{ \tt \:\dfrac{x}{y} < 0 \implies \: x > 0, \: y < 0 \: \: or \: x < 0, \: y < 0 }}$