Question 83

If 3x-5(x-1) > 2x - 1 < 2 + 4x; then x can take which of the following values?

Solution

Expression 1 : 3x-5(x-1) > 2x - 1

=> $$3x-5x+5$$ > $$2x-1$$

=> $$2x+2x$$ < $$5+1$$

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

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

Expression 2 : 2x - 1 < 2 + 4x

=> $$4x-2x$$ > $$-1-2$$

=> $$2x$$ > $$-3$$

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

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

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

=> Ans - (D)


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