The equation given in the image is:

$|x + 1| = 6$

To solve this absolute value equation, we break it into two cases:

Case 1: $x + 1 = 6$

Solve for $x$:

$x = 6 - 1 = 5$

Case 2: $x + 1 = -6$

Solve for $x$:

$x = -6 - 1 = -7$

Thus, the two solutions are:

$x = 5 \quad \text{or} \quad x = -7$

Let me know if you'd like further details or have any questions!

Here are 5 related questions for practice:

1. Solve $|x - 3| = 8$.
2. Solve $|2x + 4| = 10$.
3. What does the graph of $|x + 1|$ look like?
4. Solve $|x - 5| = 0$.
5. What happens if the right side of the absolute value equation is negative, like $|x + 1| = -2$?

Tip: When solving absolute value equations, remember to always consider both the positive and negative cases!