To find the additive inverse of a given number, we need to determine the number that, when added to the original number, results in zero.
Let's look at the expression given in Exercise 41:
[tex]\[ 6 - \pi \][/tex]
We want to find the additive inverse of [tex]\( 6 - \pi \)[/tex]. The additive inverse of a number [tex]\( a \)[/tex] is simply [tex]\( -a \)[/tex]. In other words, we need to negate the expression [tex]\( 6 - \pi \)[/tex].
1. Start with the expression:
[tex]\[ 6 - \pi \][/tex]
2. Negate the whole expression to find its additive inverse:
[tex]\[ -(6 - \pi) \][/tex]
3. Simplify the negation:
[tex]\[ -6 + \pi \][/tex]
Hence, the additive inverse of [tex]\( 6 - \pi \)[/tex] is [tex]\( -6 + \pi \)[/tex].
For a numerical approximation, we can use the given results:
- The value of [tex]\( 6 - \pi \)[/tex] is approximately [tex]\( 2.858407346410207 \)[/tex].
- Therefore, the additive inverse, [tex]\( -(6 - \pi) \)[/tex], is approximately [tex]\( -2.858407346410207 \)[/tex].
In conclusion, the additive inverse of the expression [tex]\( 6 - \pi \)[/tex] is numerically approximately [tex]\( -2.858407346410207 \)[/tex].
