For the first equation, we have:

|x + 2| - 1 = 7

Add 1 to both sides:

|x + 2| = 8

This means that x + 2 = 8 or x + 2 = -8.

If x + 2 = 8, then x = 6.
If x + 2 = -8, then x = -10.

So the solutions to the first equation are x = 6 and x = -10.

For the second equation, we have:

11 - 3 * |2x + 1| = 5

Add 3 * |2x + 1| to both sides:

11 = 5 + 3 * |2x + 1|

Subtract 5 from both sides:

6 = 3 * |2x + 1|

Divide by 3:

2 = |2x + 1|

This means that 2x + 1 = 2 or 2x + 1 = -2.

If 2x + 1 = 2, then 2x = 1 and x = 0.5.
If 2x + 1 = -2, then 2x = -3 and x = -1.5.

So the solutions to the second equation are x = 0.5 and x = -1.5.