As you analyze the equation, you need to simplify each sentences:
Machine on the tank loses - 1.5 gallons of water (an hour)
Pumped in the tank - 1 gallon (well)
= -1.5 + 1 = -.5
Tank starts to full with - 150 gallons = +150
The best equation suited in the following is: w = -.5 + 150