Find the solution set for the following inequality. \( |q+7|>1 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \{q \mid q<\square \) or \( q>\square\} \). (Simplify your answers.) B. The solution set is \( \{q \mid \square

Ask by Pritchard Schmidt. in the United States

Feb 04,2025

To solve the inequality \( |q+7| > 1 \), we need to break it down into two separate cases based on the definition of absolute value. 1. **Case 1:** \( q + 7 > 1 \) leads to \( q > -6 \). 2. **Case 2:** \( q + 7 < -1 \) leads to \( q < -8 \). Combining these results, the solution set is \( \{q \mid q < -8 \text{ or } q > -6\} \). So, the correct choice is: A. The solution set is \( \{q \mid q< -8 \) or \( q> -6\} \).