If 2x - 6 ≤ x - 3 and 1+3x < 4x + 4, then x can take which of the following values?

Question 84

Solution

Expression 1 : 2x - 6 ≤ x - 3

=> $$2x-x \leq -3+6$$

=> $$x \leq 3$$ ------------(i)

Expression 2 : 1+3x < 4x + 4

=> $$4x-3x$$ > $$1-4$$

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

=> $$x$$ > $$-3$$ -----------(ii)

Combining inequalities (i) and (ii), we get : $$-3$$ < $$x \leq 3$$

The only value that $$x$$ can take among the options = 2

=> Ans - (D)

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