Question 71

If 5x + 4(1 - x) > 3x -4 > 5x/3 - x/3; then x can take which of the following values?

Solution

Expression 1 : $$3x - 4$$ > $$\frac{5x}{3} - \frac{x}{3}$$

=> $$9x - 12$$ > $$4x$$

=> $$9x - 4x$$ > $$12$$

=> $$x$$ > $$\frac{12}{5}$$ ----------(i)

Expression 2 : $$5x + 4(1 - x)$$ > $$3x - 4$$

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

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

=> $$x$$ < $$4$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{12}{5}$$ < $$x$$ < $$4$$

Thus, only value that $$x$$ can take among the options = 3

=> Ans - (C)


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