Answer
False.
New statement:
-x -(x)=-x+x = 0
Work Step by Step
-x-x=-2x $\ne$ 0
The terms do not cancel out.
Thus the statement is false
New statement:
-x -(x)=-x+x = 0
By adding another negative sign to one of the negative terms, -x is multiplied by -1 to form +x. -x+x will add to form 0.