Answer :

Given:


.


Signs of 2x – 3:


2x – 3 = 0


(Adding 3 on both the sides and then dividing both sides by 2)


2x – 3 < 0


(Adding 3 on both the sides and then dividing both sides by 2)


2x – 3 > 0


(Adding 3 on both the sides and then dividing both sides by 2)


Signs of 3x – 7:


3x – 7 = 0


(Adding 7 on both the sides and then dividing both sides by 3)


3x – 7 < 0


(Adding 7 on both the sides and then dividing both sides by 3)


3x – 7 > 0


(Adding 7 on both the sides and then dividing both sides by 3)


Zeroes of denominator:


3x – 7 = 0



(Adding 7 on both the sides and then dividing both sides by 3)


Interval that satisfies the required condition: < 0



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