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

Question 87

Solution

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

=> $$6x+10$$ > $$4x-5$$

=> $$6x-4x$$ > $$-5-10$$

=> $$2x$$ > $$-15$$

=> $$x$$ > $$\frac{-15}{2}$$ --------(i)

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

=> $$4x-3x$$ < $$2+5$$

=> $$x$$ < $$7$$ ---------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-15}{2}$$ < $$x$$ < $$7$$

The only value that $$x$$ can take = 6

=> Ans - (B)

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