If 4x-7<x-2 and $$5x+\frac{2}{3}\geq3x+1$$; then x can take which of the following values?

Expression 1 : 4x - 7 < x - 2

=> $$4x-x$$ < $$7-2$$

=> $$3x$$ < $$5$$

=> $$x$$ < $$\frac{5}{3}$$ ------------(i)

Expression 2 : $$5x+\frac{2}{3}\geq3x+1$$

=> $$5x-3x \geq 1-\frac{2}{3}$$

=> $$2x \geq \frac{1}{3}$$

=> $$x \geq \frac{1}{6}$$ -----------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{1}{6} \leq x$$ < $$\frac{5}{3}$$

The only value that $$x$$ can take among the options = 1

=> Ans - (D)