Solve the equation: |b+4|+1=10

|b+4| = 9

There are two possibilities to solve for b:

1) b + 4 = 9
b = 5

2) -(b + 4) = 9
-b - 4 = 9
-b = 13
b = -13

Therefore, the solutions for b are b = 5 and b = -13.