The equation given in the image is:

$|x - 8| + 1 = 6$

Let's solve this step by step:

Step 1: Isolate the absolute value expression.

Subtract 1 from both sides of the equation: $|x - 8| = 6 - 1$ $|x - 8| = 5$

Step 2: Set up two cases for the absolute value equation.

By definition, $|x - 8| = 5$ means that either $x - 8 = 5$ or $x - 8 = -5$.

Case 1: $x - 8 = 5$ $x = 5 + 8$ $x = 13$

Case 2: $x - 8 = -5$ $x = -5 + 8$ $x = 3$

Step 3: Final solution

The solutions are: $x = 13 \quad \text{or} \quad x = 3$

Would you like more details on any step?

Here are 5 related questions to further your understanding:

1. What does the absolute value function represent geometrically?
2. How do you solve absolute value inequalities?
3. What happens if an absolute value equation has no solution?
4. How can you graph the solutions to this equation on a number line?
5. Can you create an absolute value equation that has only one solution?

Tip: Always isolate the absolute value expression first when solving such equations.