17. \( |b-8|+10>22 \)

To solve the inequality \( |b-8|+10>22 \), we can start by isolating the absolute value. Subtracting 10 from both sides gives us \( |b-8|>12 \). This implies two scenarios: 1. \( b-8 > 12 \) which simplifies to \( b > 20 \), 2. \( b-8 < -12 \) which simplifies to \( b < -4 \). So the solution set for the inequality is \( b < -4 \) or \( b > 20 \). In a nutshell, you’ll find that any value of \( b \) less than -4 or greater than 20 will satisfy the original inequality!