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

Question 61

Solution

Expression 1 : 2 + 2x < 5 - x/2

=> $$2x + \frac{x}{2}$$ < $$5 - 2$$

=> $$\frac{5x}{2}$$ < $$3$$

=> $$x$$ < $$\frac{6}{5}$$ ----------(i)

Expression 2 : 5x + 3 > 5 - 5x

=> $$5x + 5x$$ > $$5 - 3$$

=> $$10x$$ > $$2$$

=> $$x$$ > $$\frac{1}{5}$$ ----------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{1}{5}$$ < $$x$$ < $$\frac{6}{5}$$

Thus, the only value that $$x$$ can take = 1

=> Ans - (D)

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