Here 3(x 2)/5≤5(2 x)/3 ⇒3x 6/5≤10 5x/3⇒3x/5 6/5≤10/3 5x/3 ⇒3x/5 +5x/3≤10/3+6/5⇒9x+25x/15≤50+18/15 ⇒34x/15≤68/15 Multiplying both sides by 15, we have 34x ≤ 68 D ...

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Byju's Answer

Standard XII

Mathematics

Method of Intervals

3x-2/5≤52-x/3

Question

$\frac{3 (x - 2)}{5} \leq \frac{5 (2 - x)}{3}$

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Solution

Here $\frac{3 (x - 2)}{5} \leq \frac{5 (2 - x)}{3}$

$\Rightarrow \frac{3 x - 6}{5} \leq \frac{10 - 5 x}{3} \Rightarrow \frac{3 x}{5} - \frac{6}{5} \leq \frac{10}{3} - \frac{5 x}{3}$

$\Rightarrow \frac{3 x}{5} + \frac{5 x}{3} \leq \frac{10}{3} + \frac{6}{5} \Rightarrow \frac{9 x + 25 x}{15} \leq \frac{50 + 18}{15}$

$\Rightarrow \frac{34 x}{15} \leq \frac{68}{15}$

Multiplying both sides by 15, we have

$34 x \leq 68$ Dividing both sides by 34, we have

$x \leq 2$

Thus the solution set is $(- \infty, 2]$ .

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\frac{3 (x - 2)}{5} \leq \frac{5 (2 - x)}{3}

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\frac{3 (x - 2)}{5} \leq \frac{5 (2 - x)}{3}

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3(x−2)5≤5(2−x)3

Here 3(x−2)5≤5(2−x)3 ⇒3x−65≤10−5x3⇒3x5−65≤103−5x3 ⇒3x5+5x3≤103+65⇒9x+25x15≤50+1815 ⇒34x15≤6815 Multiplying both sides by 15, we have 34x≤68 Dividing both sides by 34, we have x≤2 Thus the solution set is (−∞,2].

$\frac{3 (x - 2)}{5} \leq \frac{5 (2 - x)}{3}$