Step 1 :The question is asking for an inequality that represents the maximum number of gigabytes Jackson can use while staying within his budget. The flat cost per month is \$44 and each gigabyte costs \$4. The total cost should be less than or equal to \$45. Therefore, the inequality should be \(44 + 4g \leq 45\).
Step 2 :The solution to the equation is \(\frac{1}{4}\). However, this is not the final answer because the question asks for an inequality, not an equation. The inequality should be \(44 + 4g \leq 45\). Since the solution to the equation is \(\frac{1}{4}\), the solution to the inequality should be \(g \leq \frac{1}{4}\).
Step 3 :Final Answer: The inequality that can be used to determine \(g\), the maximum number of gigabytes Jackson can use while staying within his budget, is \(\boxed{g \leq \frac{1}{4}}\).