What is the value of \( x \) in this proportion? \( \frac{4}{11}=\frac{-3}{x+5} \) \( x=-13 \frac{1}{4} \) \( x=-9 \frac{1}{2} \) \( x=-7 \) \( x=-3 \frac{1}{4} \)

To solve for \( x \) in the proportion \( \frac{4}{11}=\frac{-3}{x+5} \), you can cross-multiply. This gives you the equation \( 4(x + 5) = -3 \cdot 11 \). Simplifying this step-by-step: 1. \( 4(x + 5) = -33 \) 2. \( 4x + 20 = -33 \) 3. Subtract 20 from both sides: \( 4x = -53 \) 4. Finally, divide by 4: \( x = -\frac{53}{4} \) or \( x = -13.25 \). So, the correct answer is \( x = -13 \frac{1}{4} \). Now, let's consider some interesting points! Did you know that proportions are fundamental to many fields? They help in constructing models in science, ensuring food recipes come out just right, and even in financial forecasting. Understanding proportions can make you a master planner, whether you're cooking or budgeting! When working with proportions, one common mistake is to forget to properly distribute terms when cross-multiplying. It often leads to incorrect equations that are difficult to rectify. Always double-check your calculations to keep those pesky errors at bay!