Question 81

If 3x + 2 ≥ x - 1 and 2x - 4 ≤ 2 - x/3; then x can take which of the following values?

Solution

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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If 3x + 2 ≥ x - ­1 and 2x -­ 4 ≤ 2 - ­x/3; then x can take which of the following values?