Question 94

If 5x + 2 > 3x + 1 and 4(x - 4) - 2 ≤ 3x - 1, then x can take which of the following values?

Solution

Expression 1 : 5x + 2 > 3x + 1

=> $$5x-3x$$ > $$1-2$$

=> $$2x$$ > $$-1$$

=> $$x$$ > $$\frac{-1}{2}$$ ------------(i)

Expression 2 : 4(x - 4) - 2 ≤ 3x - 1

=> $$4x-16-2 \leq 3x-1$$

=> $$4x-3x \leq -1+18$$

=> $$x \leq 17$$ --------------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-1}{2}$$ < $$x \leq 17$$

The only value that $$x$$ can take among the options = 16

=> Ans - (A)

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