Solve the following system of inequalities

Given,

Subtracting 5 both side, we get

Hence, for above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0

⇒ 6 – 33x > 0 and 7x – 1 > 0

⇒ 33x < 6 and 7x > 1

and

⇒ [1]

Or

⇒ 6 – 33x < 0 and 7x – 1 < 0

⇒ 33x > 6 and 7x < 1

and

⇒ [not possible as ]

Also,

Subtracting 2 both sides, we get

Hence, for above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0

⇒ 23 – x > 0 and x – 8 > 0

⇒ x < 23 and x > 8

⇒ 8 < x < 23 [2]

Or

23 – x < 0 and x – 8 < 0

⇒ x > 23 and x < 8

⇒ 23 < x < 8 [Not possible, as 23 > 8]

From [1] and [2], it is clear that there is no solution satisfying both inequalities, hence the given system has no solution