Final answer:
To find out after how many months (M) the $25 per month service will save money compared to the $35 per month service, we need to compare the total costs for M months. The correct inequality for this comparison is 25M + 250 < 35M + 175, representing that the first service's total cost must be less than the second service's to save money.
Step-by-step explanation:
Tonya is comparing two DSL services to find out after how many months (M) subscribing to the $25 per month service will result in savings compared to the other service that charges $175 for installation and $35 per month. We need to compare the total costs of each service over M months to find the inequality that represents this situation.
The total cost of the first service after M months is $25M + $250, and the total cost of the second service after M months is $35M + $175. To save money in the long run with the first service, its total cost must be less than the total cost of the second service, leading us to the inequality:
25M + 250 < 35M + 175