If 5x - 1 < 3x + 2 and 5x + 5 > 6 - 2x; then x can take which of the following values?

Question 32

Solution

Expression 1 : 5x - 1 < 3x + 2

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

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

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

=> $$5x + 2x$$ > $$6 - 5$$ => $$7x$$ > $$1$$

=> $$x$$ > $$\frac{1}{7}$$ ---------------(ii)

Combining above 2 inequalities, we get : $$\frac{1}{7}$$ < $$x$$ < $$\frac{3}{2}$$

Thus, the only integer value that $$x$$ can take = 1

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