Solve the equation or inequalit \[ \begin{array}{l}\text { (a) }|b|=9 \\ \text { (b) }|b|<9 \\ \text { (c) }|b|>9\end{array} \]

We will solve each part step by step. (a) |b| = 9 The definition of absolute value states that |b| is the distance from b to 0 on the number line. Therefore, the equation |b| = 9 means that b is 9 units away from 0. This gives us two possibilities:   b = 9  or  b = –9 (b) |b| < 9 The inequality |b| < 9 means the distance of b from 0 is less than 9. Hence, b must be between –9 and 9:   –9 < b < 9 (c) |b| > 9 The inequality |b| > 9 means the distance of b from 0 is greater than 9. Therefore, b is either less than –9 or greater than 9:   b < –9  or  b > 9 Thus, the solutions are: (a) b = 9 or b = –9 (b) –9 < b < 9 (c) b < –9 or b > 9