Solve \( |x-7| \leq 4 \) State your answer as a compound inequality \( A \leq x \leq B \) : State your answer in interval notation \( [A, B] \) :

To solve the inequality \( |x - 7| \leq 4 \), we can interpret it as the distance between \( x \) and 7 being at most 4. This can be rewritten as a compound inequality and also expressed in interval notation. ### Step-by-Step Solution: 1. **Start with the absolute inequality:** \[ |x - 7| \leq 4 \] 2. **Rewrite the absolute inequality as a compound inequality:** \[ -4 \leq x - 7 \leq 4 \] 3. **Isolate \( x \) by adding 7 to all parts of the inequality:** \[ -4 + 7 \leq x \leq 4 + 7 \] \[ 3 \leq x \leq 11 \] ### Final Answers: - **Compound Inequality:** \[ 3 \leq x \leq 11 \] - **Interval Notation:** \[ [3,\, 11] \]