Question 90

Given: x - 5 ≤ 2x - 3 and 2x - 1/2 ≥ 5x + 2; then x can take which of the following values?

Solution

Expression 1 : x - 5 ≤ 2x - 3

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

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

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

Expression 2 : 2x - 1/2 ≥ 5x + 2

=> $$5x-2x \leq -2-\frac{1}{2}$$

=> $$3x \leq \frac{-5}{2}$$

=> $$x \leq \frac{-5}{6}$$ --------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{-2}{3} \leq x \leq \frac{-5}{6}$$

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

=> Ans - (A)

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Given: x ­- 5 ≤ 2x -­ 3 and 2x - ­1/2 ≥ 5x + 2; then x can take which of the following values?