If 3x + 2 ≥ x - 1 and 2x - 4 ≤ 2 - x/3; then x can take which of the following values?
Expression 1 : 3x + 2 ≥ x - 1
=> $$3x-x \geq -1-2$$
=> $$2x \geq -3$$
=> $$x \geq \frac{-3}{2}$$ ---------(i)
Expression 2 : 2x - 4 ≤ 2 - x/3
=> $$2x+\frac{x}{3} \leq 2+4$$
=> $$\frac{7x}{3} \leq 6$$
=> $$x \leq \frac{18}{7}$$ --------(ii)
Combining inequalities (i) and (ii), we get : $$\frac{-3}{2} \leq x \leq \frac{18}{7}$$
The only value that $$x$$ can take among the options = 1
=> Ans - (D)
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