Q. 175.0( 1 Vote )

Solve each of the following system of inequations in R

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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