Question 80

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

Solution

Expression 1 : $$5x + 2 < 4x + 1$$

=> $$5x - 4x$$ < $$1 - 2$$

=> $$x$$ < $$-1$$ ----------(i)

Expression 2 : $$2(x - 4) - 2 \leq 4x - 1$$

=> $$2x - 10 \leq 4x - 1$$

=> $$4x - 2x \geq 1 - 10$$

=> $$x \geq \frac{-9}{2}$$ ------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-9}{2} \leq x$$ < $$-1$$

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

=> Ans - (D)

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