If 3x - 4 > 2 - x/3 and 3x + 5 > 4x - 5; then ﬁnd the value of x?

Question 60

Solution

Expression 1 : 3x - 4 > 2 - x/3

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

=> $$\frac{10x}{3}$$ > $$6$$

=> $$x$$ > $$\frac{18}{10} = 1.8$$ --------(i)

Expression 2 : 3x + 5 > 4x - 5

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

=> $$x$$ < $$10$$ ---------(ii)

Combining inequalities (i) and (ii), we get : $$1.8$$ < $$x$$ < $$10$$

Thus, the only value that $$x$$ can take among the options = 7

=> Ans - (A)

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