- Define the total time spent as \(x + y\).
- Translate the phrase "45 minutes or more" into the inequality \(x + y \geq 45\).
- Compare this with the given options to confirm that \(x + y \geq 45\) is the correct representation.
- The final answer is \(\boxed{x + y \geq 45}\).
Explanation
- Analyzing the Problem Condition
The problem states that Jamaal spends \(x\) minutes practicing guitar and \(y\) minutes on homework. The total time spent on both activities is the sum of these two durations, which is \(x + y\). The condition provided is that this total time must be "45 minutes or more". In mathematics, the phrase "or more" corresponds to the "greater than or equal to" relation. Therefore, the requirement that the total time is at least 45 minutes can be written as \(x + y \geq 45\).
- Evaluating the Given Options
We examine the given options:
- \(x + y < 45\): This means the total time is strictly less than 45 minutes, which contradicts "45 minutes or more".
- \(x + y > 45\): This means the total time is strictly greater than 45 minutes, which excludes the possibility of exactly 45 minutes.
- \(x + y \leq 45\): This means the total time is 45 minutes or less, which is the opposite of the given requirement.
- \(x + y \geq 45\): This means the total time is 45 minutes or greater, which perfectly matches the condition "45 minutes or more".
Thus, the correct inequality is \(x + y \geq 45\).
Examples
This concept of inequalities is used in many everyday situations, such as when planning a study schedule. If you know that you need to spend at least 2 hours total on your school projects tonight, and you allocate \(x\) minutes to math and \(y\) minutes to science, you can model your requirement as \(x + y \geq 120\). This helps you ensure that you are meeting your minimum commitments.