Question

Find the number of integral values of which satisfy-3<2x-1<19

Answer 1

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

Given that

$\bf :\longmapsto\: - 3 < 2x - 1 < 19$

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

$\rm :\longmapsto\: - 3 + 1< 2x - 1 + 1 < 19 + 1$

$\rm :\longmapsto\: - 2 < 2x < 20$

$\red{\bf :\longmapsto\:On \: dividing \: by \: 2 \: each \: term}$

$\rm :\longmapsto\: - \dfrac{2}{2} < \dfrac{2x}{2} < \dfrac{20}{2}$

$\rm :\longmapsto\: - 1 < x < 10$

$\red{\bf :\longmapsto\:As \: x \in \: Z}$

$\rm :\implies\:x \in \{0,1,2,3,4,5,6,7,8,9 \}$

$\bf\implies \:x \: can \: take \: 10 \: integral \: values$

Additional Information :-

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

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

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

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

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

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

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

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