If 2x - 3 ≤ 5 + x and 5 - x < 1 + 5x; then x can take which of the following values?

Question 34

Solution

Expression 1 : 2x - 3 ≤ 5 + x

=> $$2x-x \leq 5+3$$

=> $$x \leq 8$$ ------------(i)

Expression 2 : 5 - x < 1 + 5x

=> $$5x+x$$ > $$5-1$$

=> $$6x$$ > $$4$$

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

Combining inequalities (i) and (ii), we get : $$\frac{2}{3}$$ < $$x \leq 8$$

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

=> Ans - (B)

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If 2x -­ 3 ≤ 5 + x and 5 -­ x < 1 + 5x; then x can take which of the following values?