To establish the inequality for Carlos's cell phone plan, we need to consider his flat monthly cost of $57 and the additional cost of $5 per gigabyte used. He wants to keep his total monthly bill under $65.
Let's define \(x\) as the number of gigabytes Carlos uses. The total cost of his plan can be expressed as:
\[ \text{Total Cost} = 57 + 5x \]
Since Carlos wants his bill to be less than $65, we can set up the following inequality:
\[ 57 + 5x < 65 \]
Now, we'll solve the inequality:
- Subtract 57 from both sides:
\[ 5x < 65 - 57 \]
\[ 5x < 8 \]
- Divide both sides by 5:
\[ x < \frac{8}{5} \]
\[ x < 1.6 \]
Since \(x\) represents the number of gigabytes, we can only use whole numbers (0, 1, etc.). Therefore, the maximum whole number of gigabytes Carlos can use while staying under $65 is 1 GB.
Inequality: \[ x < 1.6 \] and the practical solution for \(x\) is \(x \leq 1\) (in whole numbers).