If 3(2 - 3x) < 2 - 3x ≥ 4x -6; then x can take which of the following values?

Question 35

Solution

Expression 1 : 3(2 - 3x) < 2 - 3x

=> $$6-9x$$ < $$2-3x$$

=> $$9x-3x$$ > $$6-2$$

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

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

Expression 2 : 2 - 3x ≥ 4x -6

=> $$4x+3x \leq 2+6$$

=> $$7x \leq 8$$

=> $$x \leq \frac{8}{7}$$ -----------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{2}{3}$$ < $$x \leq \frac{8}{7}$$

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

=> Ans - (D)

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