Given: 6x + 2(6-x) > 2x -2 < 5x/2 - 3x/4; then x can take which of the following values?

Expression 1 : $$2x - 2 < \frac{5x}{2} - \frac{3x}{4}$$

=> $$2x - 2$$ < $$\frac{7x}{4}$$

=> $$8x - 8$$ < $$7x$$

=> $$8x - 7x$$ < $$8$$

=> $$x$$ < $$8$$ ----------(i)

Expression 2 : $$6x + 2(6 - x)$$ > $$2x - 2$$

=> $$4x + 12$$ > $$2x - 2$$

=> $$4x - 2x$$ > $$-12 - 2$$

=> $$2x$$ > $$-14$$

=> $$x$$ > $$-7$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$-7$$ < $$x$$ < $$8$$

Thus, only value that $$x$$ can take among the options = 5

=> Ans - (C)