Solve the equation or inequality. Write the solution set to (a) \( |b|=2 \) (b) \( |b|<2 \) (c) \( |b|>2 \)

We are given absolute value expressions and need to solve the equation/inequalities for b. (a) |b| = 2 The absolute value equals 2 if b is 2 or -2. Solution: b = 2 or b = -2. (b) |b| < 2 The inequality |b| < 2 means that the distance from b to 0 is less than 2. This implies b lies between -2 and 2. Solution: -2 < b < 2. (c) |b| > 2 The inequality |b| > 2 means that b is more than 2 units away from 0. This occurs when b is either less than -2 or greater than 2. Solution: b < -2 or b > 2. Thus, the solution sets are: (a) { -2, 2 } (b) (-2, 2) (c) (-∞, -2) ∪ (2, ∞)