If 2x - 3(2x - 2) > x - 1 < 2 + 2x; then x can take which of the following values?

Question 71

Solution

Expression 1 : $$x - 1 < 2 + 2x$$

=> $$2x - x$$ > $$-1 - 2$$

=> $$x$$ > $$-3$$ ----------(i)

Expression 2 : $$2x - 3(2x - 2)$$ > $$x - 1$$

=> $$-4x + 6$$ > $$x - 1$$

=> $$4x + x$$ < $$6 + 1$$

=> $$x$$ < $$\frac{7}{5}$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$-3$$ < $$x$$ < $$\frac{7}{5}$$

Thus, only value that $$x$$ can take among the options = -2

=> Ans - (B)

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