The inequality can be simplified to:
-7 < x < 3
And the graph can be seen in the image at the end.
How to solve the inequality?
Here we have the inequality:
|x + 2| + 1 > 6
To solve this, we need to isolate the variable x, so if we first subtract 1 we get:
|x + 2| +1 - 1 > 6 - 1
|x + 2| > 5
The absolute value part can be decomposed into two.
-5 < x + 2 < 5
Now we can subtract 2 in all the inequality, so we get:
-5 - 2 < x + 2 - 2 < 5 - 2
-7 < x < 3
The graph of this can be seen below