If 2 + 2x < 3 + 5x and 3(x - 2)2 < 5 - x; then x can take which of the following values?

Question 80

If $$2 + 2x < 3 + 5x$$ and $$3(x - 2)2 < 5 - x$$; then x can take which of the following values?

Solution

Expression 1 : $$2 + 2x < 3 + 5x$$

=> $$5x - 2x$$ > $$2 - 3$$

=> $$x$$ > $$\frac{-1}{3}$$ ----------(i)

Expression 2 : $$3(x - 2)2 < 5 - x$$

=> $$6x - 12$$ < $$5 - x$$

=> $$6x + x$$ < $$5 + 12$$

=> $$x$$ < $$\frac{17}{7}$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-1}{3}$$ < $$x$$ < $$\frac{17}{7}$$

Thus, $$x$$ can take values = 0 , 1 , 2

=> Ans - (A)

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