Given: 2x - 4 ≤ 2 - x/3 and 2(2x + 5) > 3x - 5, then x can take which of the following values?

Question 81

Solution

Expression 1 : 2x - 4 ≤ 2 - x/3

=> $$2x+\frac{x}{3} \leq 2+4$$

=> $$\frac{7x}{3} \leq 6$$

=> $$x \leq \frac{18}{7}$$ ------------(i)

Expression 2 : 2(2x + 5) > 3x - 5

=> $$4x+10$$ > $$3x-5$$

=> $$4x-3x$$ > $$-5-10$$

=> $$x$$ > $$-15$$ -----------(ii)

Combining inequalities (i) and (ii), we get : $$-15$$ < $$x \leq \frac{18}{7}$$

The only value that $$x$$ can take among the options = -14

=> Ans - (A)

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