Question 77

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

Solution

Expression 1 : x + 3 ≤ 4x + 4

=> $$4x-x \geq 3-4$$

=> $$3x \geq -1$$

=> $$x \geq \frac{-1}{3}$$ ---------(i)

Expression 2 : 3(4 - x) - 4 ≥ 2x - 2

=> $$12-3x-4 \geq 2x-2$$

=> $$2x+3x \leq 8+2$$

=> $$5x \leq 10$$

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

Combining inequalities (i) and (ii), we get : $$\frac{-1}{3} \leq x \leq 2$$

The only value that $$x$$ can take among the options = 1

=> Ans - (A)

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