The mathematical sentence 'g + 7 = 12' represents a simple linear equation where 'g' is the variable that stands for the initial number of gallons of gas in the tank. The equation states that when you add 7 gallons to the initial amount of gas (g), the total equals 12 gallons. To solve for 'g', you would subtract 7 from both sides of the equation, resulting in 'g = 12 - 7', which simplifies to 'g = 5'. This means there were initially 5 gallons of gas in the tank.