If 5(4-x)-4>5x-2>2x-6, then the value of x is

Question 29

If $$5(4-x)-4>5x-2>2x-6$$, then the value of x is

Solution

Expression 1: $$5(4 - x) - 4$$ > $$5x - 2$$

=> $$20 - 5x - 4$$ > $$5x - 2$$

=> $$5x + 5x$$ < $$16 + 2$$

=> $$x$$ < $$\frac{18}{10}$$ ------------(i)

Expression 2 : $$5x - 2$$ > $$2x - 6$$

=> $$5x - 2x$$ > $$2 - 6$$

=> $$x$$ > $$\frac{-4}{3}$$ ----------(ii)

Combining inequalities (i) and (ii),we get : $$\frac{-4}{3}$$ < $$x$$ < $$\frac{18}{10}$$

Thus, $$x$$ can take values = -1 , 0 , 1

=> Ans - (C)

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