\( \dfrac{3(x – 2)}{5}≤ \dfrac{5(x – 2)}{3}\)

Now by cross – multiplying the denominators, we get

9(x- 2) ≤ 25 (2 – x)

9x – 18 ≤ 50 – 25x

Now adding 25x both the sides,

9x – 18 + 25x ≤ 50 – 25x + 25x

34x – 18 ≤ 50

Adding 25x both the sides,

34x – 18 + 18 ≤ 50 + 18

34x ≤ 68

Dividing both sides by 34,

\( \dfrac{34}{34} ≤\dfrac{68}{34}\)

x ≤ 2

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

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

Answered by Pragya Singh | 1 year agoSolve each of the following in equations and represent the solution set on the number line \( \dfrac{5x}{4}-\dfrac{4x-1}{3}>1,\) where x ϵ R.

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