Question 83

If 2 + 4x < 5 - x/2 and 3x + 3 > -5 - 3x; then x can take which of the following values?

Solution

Expression 1 : $$2 + 4x < 5 - \frac{x}{2}$$

=> $$4x + \frac{x}{2}$$ < $$5 - 2$$

=> $$\frac{9x}{2}$$ < $$3$$

=> $$x$$ < $$\frac{2}{3}$$ ----------(i)

Expression 2 : $$3x + 3$$ > $$-5 - 3x$$

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

=> $$x$$ > $$\frac{-4}{3}$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-4}{3}$$ < $$x$$ < $$\frac{2}{3}$$

Thus, only value that $$x$$ can take among the options = -1

=> Ans - (D)


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