An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.

The current rate is simply equal to $175 per month, let us call this as rate A:

A = 175

The new rate is $94 plus $4.50 per devices, let us call this as rate B:

B = 94 + 4.50 x

where x is the number of devices connected to the network

The inequality equation for us to find x which the new plan is less than current plan is:

94 + 4.50 x < 175

Solving for x:

4.50 x < 81

x < 18

So the number of devices must be less than 18.

- From the graph, we can actually see that the new rate intersects the current rate at number of devices equal to 18. So it should really be below 18 devices.