We are given the equation:

$|5 + b| = 1$

To solve for $b$, we need to handle the absolute value expression. The absolute value equation $|x| = a$ has two solutions: $x = a$ or $x = -a$.

So, in this case, we solve the following two equations:

1. $5 + b = 1$
2. $5 + b = -1$

Solving equation 1:

$5 + b = 1$ Subtract 5 from both sides: $b = 1 - 5$ $b = -4$

Solving equation 2:

$5 + b = -1$ Subtract 5 from both sides: $b = -1 - 5$ $b = -6$

Solution:

The values of $b$ are $-4$ and $-6$.

Do you want further details or have any questions?

Here are 5 related questions:

1. How do you solve absolute value inequalities?
2. What happens when the right-hand side of an absolute value equation is negative?
3. Can you graph the function $f(b) = |5 + b|$?
4. What is the difference between absolute value equations and inequalities?
5. How do you simplify expressions involving multiple absolute values?

Tip: Always check both cases (positive and negative) when solving absolute value equations!