Final answer:
The most miles you could ride in the taxi without using all of your money is 15 miles.
Step-by-step explanation:
To determine the most miles you could ride in the taxi without using all of your money, you can use an inequality.
Let's assume the number of miles you can ride in the taxi is represented by 'm'. The inequality that represents this situation is:
5 + 0.60m <= 14
This inequality states that the cost of the ride ($5 plus $0.60 per mile) should be less than or equal to the amount of money you have ($14).
To find the maximum number of miles you can ride, we need to solve this inequality. Subtracting 5 from both sides gives us:
0.60m <= 9
Next, divide both sides of the inequality by 0.60 to isolate 'm':
m <= 15
This means that the most miles you could ride in the taxi without using all of your money is 15 miles.