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

Question 46

Solution

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

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

=> $$x$$ > $$-6$$ ----------(i)

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

=> $$4x - 8$$ < $$2x - 3$$

=> $$4x - 2x$$ < $$8 - 3$$

=> $$x$$ < $$\frac{5}{2}$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$-6$$ < $$x$$ < $$\frac{5}{2}$$

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

=> Ans - (A)

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