Question 71

If 2x + 2(4 + 3x) < 2 + 3x > 2x + x/2; then x can take which of the following values?

Solution

Expression 1 : $$2 + 3x$$ > $$2x + \frac{x}{2}$$

=> $$4 + 6x$$ > $$5x$$

=> $$6x - 5x$$ > $$-4$$

=> $$x$$ > $$-4$$ ----------(i)

Expression 2 : $$2x + 2(4 + 3x) < 2 + 3x$$

=> $$8x + 8$$ < $$2 + 3x$$

=> $$8x - 3x$$ < $$2 - 8$$

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

Combining inequalities (i) and (ii), we get : $$-4$$ < $$x$$ < $$\frac{-6}{5}$$

Thus, only value that $$x$$ can take among the options = -3

=> Ans - (A)


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