Solve each of the following in equations and represent the solution set on the number line.
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Given:
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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
1