If 5x - 4 ≤ 2 - x and 4x + 5 > 2x - 5, then x can take which of the following values?

Question 58

Solution

Expression 1 : 5x - 4 ≤ 2 - x

=> $$5x + x \leq 2 + 4$$ => $$6x \leq 6$$

=> $$x \leq 1$$ ---------(i)

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

=> $$4x - 2x$$ > $$-5 -5$$ => $$2x$$ > $$-10$$

=> $$x$$ > $$-5$$ ----------(ii)

Combining inequalities (i) and (ii), we get : $$-5$$ < $$x \leq 1$$

Thus, $$x$$ can take values = -4 , -3 , -2 , -1 , 0 , 1

=> Ans - (D)

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