The additive inverse of an integer x is 2x.
Step 1: Recall the meaning of “additive inverse”.
The additive inverse of a number is the number you add to it to get zero.
In symbols:
If the number is (x), we want another number (y) such that
(x + y = 0).
Step 2: Find the number that makes the sum zero.
To make (x + y = 0), the correct choice is (y = -x), because
(x + (-x) = 0).
Step 3: Check the claim “additive inverse of (x) is (2x)”.
If we try (2x) instead, the sum becomes
(x + 2x = 3x).
(3x = 0) only when (x = 0). For any other (x), this is not zero.
Step 4: Quick example.
Let (x = 5).
(5 + (-5) = 0) ✓ (so (-5) is the additive inverse)
(5 + 2cdot 5 = 5 + 10 = 15 eq 0) ✗ (so (2x) is not the additive inverse)
Conclusion: The additive inverse of (x) is (-x), not (2x). Therefore, the statement is false.