Question 34

For what range of values of 'x', will be the inequality $$15x - \left(\frac{2}{x}\right) > 1$$?

Solution

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We have 
$$15x-\frac{2}{x}>1$$

Multiple by x on both sides considering x>0

⇒ $$15x^2-2>x$$
⇒$$15x^2-x-2>0$$
⇒$$15x^2-6x+5x-2>0$$
⇒ (3x+1)(5x-2)>0
we get x>2/5 or x<-1/3 but this is not considered as we have taken x>0

If x<0 the sign of inequality will reverse, and for it to be satisfied we will get the values of x between -1/3<x<0

Hence, the answer is Option D

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