Solve the given inequality for real x:  $$\dfrac{3(x – 2)}{5}≤ \dfrac{5(x – 2)}{3}$$

Asked by Pragya Singh | 1 year ago |  94

##### Solution :-

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

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

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 ago

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