Final answer:
The inequality to determine the max number of gigabytes Damian can use within his budget is $44 + $3x \leq $45, which simplifies to x \leq $\frac{1}{3}$ after solving.
Step-by-step explanation:
The question asks which inequality we can use to determine x, the maximum number of gigabytes Damian can use while keeping his monthly cell phone bill under $45. The cell phone plan has a flat cost of $44 per month, plus an additional $3 per gigabyte of data used. Damian wants to keep his total monthly cost less than or equal to $45. The correct inequality that represents this scenario is Option 1: $44 + $3x \leq $45. To solve this inequality, we subtract $44 from both sides to get $3x \leq $1. Dividing both sides by $3, we find that x, the maximum number of gigabytes he can use without exceeding his budget, is \leq $\frac{1}{3}$. This means Damian cannot use more than $\frac{1}{3}$ of a gigabyte in addition to his flat rate to stay within his budget.
In order to determine the maximum number of gigabytes Damian can use while staying within his budget, we can set up an inequality based on the given information. Damian pays a flat cost of $44 per month and an additional $3 per gigabyte. Let's assume xx represents the maximum number of gigabytes Damian can use while staying within his budget.
The total cost of his phone plan can be represented as: $44 + $3x, where x is the number of gigabytes. We want to keep his bill under $45 per month, so we can set up the following inequality: $44 + $3x ≤ $45.
This inequality states that the total cost of Damian's phone plan (the sum of the flat cost and the cost per gigabyte) must be less than or equal to $45 in order for him to stay within his budget.