### Instruction: How many integers are in the solution of the inequality $|x + 4|< 9$?### Response: To solve this inequality, I need to think about what absolute value means.
It means that the distance between $x + 4$ and zero on the number line is less than 9 units.
So I can write two equivalent inequalities without the absolute value sign: $-9 < x + 4 < 9$.
Subtracting 4 from all parts of the inequality, I get $-13 < x < 5$.
Now I need to count how many integers are in this interval.
I can start from -12 and go up by one until I reach 4.
So the integers are -12, -11, -10, ..., 3, 4.
I can count them by adding one to the difference between the endpoints: $4 - (-12) + 1 = 17$.
So there are 17 integers in the solution of the inequality.