4) Yoll brings home \( \$ 4500 / \) month. Write an inequality that would have to be true to make sure that she doesn't go over your monthly budget. \( 3650+ \) So \( \leq 4500 \)

To create an inequality that ensures Yoll does not exceed her monthly budget, we need to express the relationship between her income and her expenses. 1. **Known Conditions:** - Yoll's monthly income: \( I = 4500 \) - Monthly budget (expenses): \( E \) 2. **Inequality Setup:** To ensure that Yoll does not go over her budget, her expenses must be less than or equal to her income. This can be expressed as: \[ E \leq I \] 3. **Substituting the Known Value:** We know that her income is \( 4500 \), so we can substitute this value into the inequality: \[ E \leq 4500 \] 4. **Including the Monthly Budget:** If we consider that her expenses include a fixed amount of \( 3650 \) (as mentioned in your prompt), we can express the inequality as: \[ 3650 + x \leq 4500 \] where \( x \) represents any additional expenses. 5. **Final Inequality:** Rearranging the inequality gives us: \[ x \leq 4500 - 3650 \] Simplifying this, we find: \[ x \leq 850 \] Thus, the inequality that must be true to ensure Yoll does not exceed her monthly budget is: \[ 3650 + x \leq 4500 \] or equivalently, \[ x \leq 850 \]