Problem Solving

p = | x - 2 | + | x +2 |

Consider the above equation for the following discussion

Is it ok to form the following combinations while trying to interpret the value of p?

Form combinations like
P= -(x-2)+(x+2) = 4
P=-(x-2)-(x+2) = -2x-4
P=+(x-2)-(x+2) = -4
P=+(x-2)+(x+2)= 2x

Well your third equation is definitely inaccurate. We know at a minimum that the sum in question is not negative since absolute value is never negative.

It looks to me like a better bet is to consider values between 2 and -2, in which case the answer is always 4, vs. values outside of that range which come to the absolute value of 2x.

I'm interested in what the problem might be asking for?