Question

3(x-2)/5≤5(2-x)/3 x ka Man gyat kijiye​

Answer 1

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$= > \frac{3(x - 2)}{5} \leqslant \frac{5(2 - x)}{3} \\ \\ = > \frac{3x - 6}{5} \leqslant \frac{10 - 5x}{3} \\ \\ = > 9x - 18 \leqslant 50 - 25x \: \: \: \: \: \: .....(ii)\\ \\ = > 9x + 25x = 50 \times 18 \\ \\ = > 34x = 68 \\ \\ = > x = \frac{68}{34} \\ \\ = > x = 2 \: \: \: \: \: \: \: \: \: \: \: \: ............(ii)\\ \\ subtituting \: (ii) \: in \: (i).. \\ we \: have \: \\ \\ 18 - 18 = 50 - 50 \\ \\ 0 = 0 \\ \\ hence.. \: they \: are \: equal$

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Answer 2

${ \bold{ \underline{Given} : - }} \\ \\ = > \frac{3(x - 2)}{5} \leqslant \frac{5(2 - x)}{ 3 } \\ \\ { \bold{ \underline{To \: \: find} : - }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Value \: \: of \: \: 'x' \\ \\ { \bold{ \underline{ Solution} : - }} \\ \\ = > \frac{3(x - 2)}{5} \leqslant \frac{5(2 - x)}{3} \\ \\ = > 9(x - 2) \leqslant 25(2 - x) \\ \\ = > 9x - 18 \leqslant 50 - 25x \\ \\ = > 25x + 9x \leqslant 50 + 18 \\ \\ = > 34x \leqslant 68 \\ \\ = > x \leqslant 2 \\ \\ \: \: { \bold{So \: \: that - }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \bold{ \boxed{x \in ( - \infty \: ,\: 2 ] }}} \\ \\ { \bold{ \underline{ Properties \: \: of \: \: inequalities } : - }} \\ \\ (1) \: \: Addition \: \: Property \: \: of \: \: Inequality. \\ \\ (2) \: \: Subtraction \: \: Property \: \: of \: \: Inequality .\\ \\ (3) \: \: Multiplication \: \: Property \: \: of \: \: Inequality .\\ \\ (4) \: \: Division \: \: Property \: \: of \: \: Inequality. \\ \\ { \bold{ \underline{Note} : - }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: Multiplication \: \: Property \: \: of \: \: Inequality \: \: can \: \: use \\ for \: \: known \: \: variable.$