2. \( \frac{8 x+5}{11}-9 \) for \( x=-2 \)

To evaluate the expression \( \frac{8 x+5}{11}-9 \) for \( x=-2 \), we first substitute \(-2\) into the equation. Starting with the substitution, we have: \[ \frac{8(-2)+5}{11}-9 = \frac{-16+5}{11}-9 = \frac{-11}{11}-9 = -1-9 = -10. \] So, the value of the expression when \( x=-2 \) is \(-10\). Now, let's dive a little deeper! The expression involves linear operations and is quite common in algebra. Knowing how to manipulate such expressions can help simplify many real-world situations, like calculating profits or analyzing trends where linear relationships are observed. Additionally, common mistakes people make with such expressions include not following the order of operations properly, especially when multiple operations are involved. It’s important to simplify inside the parentheses and handle fractions diligently before subtracting or adding, to avoid small errors that can lead to incorrect results!