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

1 thought on “Find the number of integral values of which satisfy-3<2x-1<19”

1. [tex]\large\underline{\sf{Solution-}}[/tex]

   Given that

   [tex]\bf :\longmapsto\: – 3 < 2x – 1 < 19[/tex]

   [tex] \red{\bf :\longmapsto\:On \: adding \: 1 \: in \: each \: term}[/tex]

   [tex]\rm :\longmapsto\: – 3 + 1< 2x – 1 + 1 < 19 + 1[/tex]

   [tex]\rm :\longmapsto\: – 2 < 2x < 20[/tex]

   [tex] \red{\bf :\longmapsto\:On \: dividing \: by \: 2 \: each \: term}[/tex]

   [tex]\rm :\longmapsto\: – \dfrac{2}{2} < \dfrac{2x}{2} < \dfrac{20}{2} [/tex]

   [tex]\rm :\longmapsto\: – 1 < x < 10[/tex]

   [tex] \red{\bf :\longmapsto\:As \: x \in \: Z}[/tex]

   [tex]\rm :\implies\:x \in \{0,1,2,3,4,5,6,7,8,9 \}[/tex]

   [tex]\bf\implies \:x \: can \: take \: 10 \: integral \: values[/tex]

   Additional Information :-

   [tex]\boxed{ \green{ \tt \:x > y \implies \: – x < – y }}[/tex]

   [tex]\boxed{ \green{ \tt \:x < y \implies \: – x > – y }}[/tex]

   [tex]\boxed{ \green{ \tt \:x \geqslant y \implies \: – x \leqslant – y }}[/tex]

   [tex]\boxed{ \green{ \tt \:x \leqslant y \implies \: – x \geqslant – y }}[/tex]

   [tex]\boxed{ \green{ \tt \: – x > y \implies \: x < – y }}[/tex]

   [tex]\boxed{ \green{ \tt \: – x < y \implies \: x > – y }}[/tex]

   [tex]\boxed{ \green{ \tt \:\dfrac{x}{y} > 0 \implies \: x > 0, \: y > 0 \: or \: x < 0, \: y < 0 }}[/tex]

   [tex]\boxed{ \green{ \tt \:\dfrac{x}{y} < 0 \implies \: x < 0, \: y > 0 \: or \: x > 0, \: y < 0 }}[/tex]

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