Let's begin by listing out the information given to us:
Site A: $4.95 per month, $49.95 startup fee
Site B: $9.95 per month, $0 startup fee
The inequality which indicates the number of months Ian could use Site B while having his cost less than Site A is given by:
[tex]\begin{gathered} A\colon y=4.95m+49.95----1 \\ B\colon y=9.95m--------2 \\ To\text{ solve for m, we equate Equations 1 \& 2. We have:} \\ 4.95m+49.95=9.95m \\ \text{Subtract 4.95m from both sides, we have:} \\ 4.95m-4.95m+49.95=9.95m-4.95m\Rightarrow49.95=5m \\ 49.95=5m\Rightarrow5m=49.95 \\ 5m=49.95\Rightarrow\frac{5m}{5}=\frac{49.95}{5}\Rightarrow9.99 \\ m=9.99months \\ m\approx10months \end{gathered}[/tex]At 10 months, the cost of hosting on both Sites A & B is equal
After more than 10 months, the cost of hosting on Site A is less than Site B
At less than 10 months, the cost of hosting on Site A is more than Site B
Therefore, Ian will need to keep the Site B for less than 10 months to have a cost lower than that of Site A. This is represented by the inequality:
[tex]4.95m+49.95>9.95m[/tex]Hence, option A is the correct answer
