Answer :

Given and


Let us consider the first inequality.










For this inequation to be true, there are two possible cases.


i. 11x – 2 > 0 and 7x – 1 < 0


11x – 2 + 2 > 0 + 2 and 7x – 1 + 1 < 0 + 1


11x > 2 and 7x < 1




However,


Hence, this case is not possible.


ii. 11x – 2 < 0 and 7x – 1 > 0


11x – 2 + 2 < 0 + 2 and 7x – 1 + 1 > 0 + 1


11x < 2 and 7x > 1




However,


Hence, (1)


Now, let us consider the second inequality.









For this inequation to be true, there are two possible cases.


i. x – 23 > 0 and x – 8 < 0


x – 23 + 23 > 0 + 23 and x – 8 + 8 < 0 + 8


x > 23 and x < 8


x (23, ∞) (–∞, 5)


However, (23, ∞) (–∞, 5) =


Hence, this case is not possible.


ii. x – 23 < 0 and x – 8 > 0


x – 23 + 23 < 0 + 23 and x – 8 + 8 > 0 + 8


x < 23 and x > 8


x (–∞, 23) (8, ∞)


However, (–∞, 23) (8, ∞) = (8, 23)


Hence, x (8, 23) (2)


From (1) and (2), we get



x


Thus, there is no solution of the given system of inequations.


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