If 4 + 2x ≤ 6 + x and 2x + 5 < 2 + 4x; then x can take which of the following values?

Question 78

Solution

Expression 1 : 4 + 2x ≤ 6 + x

=> $$2x-x \leq 6-4$$

=> $$x \leq 2$$ ------------(i)

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

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

=> $$2x$$ > $$3$$

=> $$x$$ > $$\frac{3}{2}$$ -----------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{3}{2}$$ < $$x \leq 2$$

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

=> Ans - (D)

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