Solve for all values of b*b* in simplest form.

open vertical bar, 5, plus, b, close vertical bar, equals, 1

∣5+*b*∣=

1

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!

Solve for all values of b in simplest form. ∣5 + b∣ = 1

Learn how to solve the absolute value equation |5 + b| = 1 with a detailed step-by-step solution. This problem covers algebraic concepts, including the handling of absolute value equations and the theorem |x| = a. Suitable for students in Grades 8-10.

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