For any integer [tex]\( a \)[/tex], [tex]\(-1 \times a \)[/tex] is equal to [tex]\(-a\)[/tex].
Here's a detailed, step-by-step explanation:
1. Understanding the multiplication by [tex]\(-1\)[/tex]:
- When you multiply any number by [tex]\(-1\)[/tex], the result is the negation of that number.
- The negation of a number changes its sign. If the number is positive, it becomes negative, and if it is negative, it becomes positive.
2. Examples for clarity:
- If [tex]\( a \)[/tex] is a positive integer, for example, [tex]\( a = 5 \)[/tex]:
[tex]\[
-1 \times 5 = -5
\][/tex]
In this case, [tex]\( -5 \)[/tex] is the negation of [tex]\( 5 \)[/tex].
- If [tex]\( a \)[/tex] is a negative integer, for example, [tex]\( a = -7 \)[/tex]:
[tex]\[
-1 \times (-7) = 7
\][/tex]
In this case, [tex]\( 7 \)[/tex] is the negation of [tex]\( -7 \)[/tex].
3. General case:
- For any integer [tex]\( a \)[/tex], multiplying [tex]\( a \)[/tex] by [tex]\(-1\)[/tex] results in:
[tex]\[
-1 \times a = -a
\][/tex]
- This holds true regardless of whether [tex]\( a \)[/tex] is positive, negative, or zero.
So, summarizing the result:
[tex]\[
\boxed{-1 \times a = -a}
\][/tex]
