Write the integer which is its own additive inverse.
\(0\)
The additive inverse of a number is the number you add to it to get zero.
In symbols: ( a + (!-a) = 0 ).
We are asked to find an integer ( x ) that is its own additive inverse.
That means: ( x = -x ).
Add ( x ) to both sides:
( x + x = 0 )
( 2x = 0 )
Divide both sides by ( 2 ):
( x = 0 )
Check:
( 0 + 0 = 0 ) ✓
Conclusion: The only integer that equals its own additive inverse is ( 0 ).