According to the question,
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
⇒ x < 2/11 and x > 1/7
⇒ 1/7 < x < 2/11 …(i)
Or
⇒ 6 – 33x < 0 and 7x – 1 < 0
⇒ 33x > 6 and 7x < 1
⇒ x > 2/11 and x < 1/7
⇒ 2/11< x < 1/7 …(which is not possible since 1/7 > 2/11)
Also,
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 …(ii)
Or
23 – x < 0 and x – 8 < 0
⇒ x > 23 and x < 8
⇒ 23 < x < 8 …(which is not possible, as 23 > 8]
Therefore, from equations (i) and (ii), we infer that there is no solution satisfying both inequalities.
Hence, the given system has no solution.
