Which of the following is not the additive inverse of \(a\)?
–(–a)
\(a\times(-1)\)
–a
\(a\div(-1)\)
Idea: The additive inverse of a number is the number you add to it to get 0.
For (a), the additive inverse is (-a) because:
(a + (-a) = 0)
Check each option:
(a) (-(-a))
First, the negative of (a) is (-a).
Now, the negative of (-a) is (-(-a)).
(-(-a) = a) (a negative of a negative becomes positive).
So (a) equals (a), not (-a). This is not the additive inverse.
(b) (a imes (-1))
(a imes (-1) = -a)
This is the additive inverse.
(c) (-a)
This is already (-a), so it is the additive inverse.
(d) (a div (-1))
(a div (-1) = -a)
This is the additive inverse.
Answer: (a) (-(-a)) is not the additive inverse of (a) because it equals (a), not (-a).