Solve the absolute inequality \( \begin{array}{l}|x+5|>3 \\ \text { a) }(-8,-2) \\ \text { b) }(-\infty,-8) \cup(-2, \infty) \\ \text { c) }(-2, \infty) \\ \text { d) }(-\infty,-8] \cup[-2, \infty)\end{array} \)

To solve the absolute inequality \( |x+5| > 3 \), we start by rewriting it in two separate inequalities: 1. \( x + 5 > 3 \) 2. \( x + 5 < -3 \) Now, we solve each inequality: 1. For \( x + 5 > 3 \): \[ x > 3 - 5 \] \[ x > -2 \] 2. For \( x + 5 < -3 \): \[ x < -3 - 5 \] \[ x < -8 \] Combining the results gives us: \[ x < -8 \quad \text{or} \quad x > -2 \] In interval notation, the solution can be expressed as: \[ (-\infty, -8) \cup (-2, \infty) \] Thus, the correct answer is **b)** \((- \infty, -8) \cup (-2, \infty)\).