If 7 + 3x ≥ 5 - x/2 and 2x + 3 ≤ 5 - 2x; then x can take which of the following values?

Expression 1 : 7 + 3x ≥ 5 - x/2

=> $$3x + \frac{x}{2} \geq 5 - 7$$

=> $$\frac{7x}{2} \geq -2$$

=> $$x \geq \frac{-4}{7}$$ ---------(i)

Expression 2 : 2x + 3 ≤ 5 - 2x

=> $$2x + 2x \leq 5 - 3$$

=> $$4x \leq 2$$

=> $$x \leq \frac{2}{4} = \frac{1}{2}$$ ----------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-4}{7} \leq x \leq \frac{1}{2}$$

Thus, the only possible value that $$x$$ can take among the given options = 0

=> Ans - (A)