Question 61
If 2 + 2x < 5 - x/2 and 5x + 3 > 5 - 5x; then x can take which of the following values?
Solution
Expression 1 : 2 + 2x < 5 - x/2
=> $$2x + \frac{x}{2}$$ < $$5 - 2$$
=> $$\frac{5x}{2}$$ < $$3$$
=> $$x$$ < $$\frac{6}{5}$$ ----------(i)
Expression 2 : 5x + 3 > 5 - 5x
=> $$5x + 5x$$ > $$5 - 3$$
=> $$10x$$ > $$2$$
=> $$x$$ > $$\frac{1}{5}$$ ----------(ii)
Combining inequalities (i) and (ii), we get : $$\frac{1}{5}$$ < $$x$$ < $$\frac{6}{5}$$
Thus, the only value that $$x$$ can take = 1
=> Ans - (D)
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