If 4(2x+3)>5-x and 5x -­3(2x­-7)>3x-­1, then x can take which of the following values?

Expression 1 : 4(2x+3)>5-x

=> $$8x+12$$ > $$5-x$$

=> $$8x+x$$ > $$5-12$$

=> $$9x$$ > $$-7$$

=> $$x$$ > $$\frac{-7}{9}$$ -----------(i)

Expression 2 : 5x -­3(2x­-7)>3x-­1

=> $$5x-6x+21$$ > $$3x-1$$

=> $$3x+x$$ < $$21+1$$

=> $$4x$$ < $$22$$

=> $$x$$ < $$\frac{11}{2}$$ ----------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-7}{9}$$ < $$x$$ < $$\frac{11}{2}$$

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

=> Ans - (C)