Find number of real solutions of:
|x+4| + |3x+2| + 10 = 0

Solution:

Absolute value is always non-negative.

So:

|x+4| ≥ 0
|3x+2| ≥ 0

Therefore:

|x+4| + |3x+2| + 10 ≥ 10

It can never become 0.

Hence, no real solution exists.

Answer: 0