Solve the given inequality for real x: \( \dfrac{(2x-1)}{3}≥\dfrac{(3x-2)}{4}-\dfrac{(2-x)}{5}\)

Asked by Pragya Singh | 1 year ago |  87

1 Answer

Solution :-

\( \dfrac{(2x-1)}{3}≥\dfrac{(3x-2)}{4}-\dfrac{(2-x)}{5}\)

\( \dfrac{(2x-1)}{3}≥\dfrac{5(3x-2)-4(2-x)}{20}\)

\( \dfrac{(2x-1)}{3}≥\dfrac{15x-10-8+4x}{20}\)

\( \dfrac{(2x-1)}{3}≥\dfrac{19x-18}{20}\)

\( 20(2x-1)≥3(19x-18)\)

\(40x-20≥57x-54\)

\(-20+54≥57x-40x\)

\(34≥17x\)

\(2≥x\)

Thus, all real numbers x, which are less than or equal to 2, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (-∞, 2]

Answered by Abhisek | 1 year ago

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