To address this problem, we need to carefully translate the phrase "the product of [tex]\( k \)[/tex] and 6."
1. Understanding the phrase:
- "Product" in mathematical terms refers to the result of multiplication.
- Therefore, the phrase "the product of [tex]\( k \)[/tex] and 6" indicates that we need to multiply [tex]\( k \)[/tex] by 6.
2. Writing the expression:
- Multiplying [tex]\( k \)[/tex] by 6 can be written algebraically as [tex]\( 6k \)[/tex].
To evaluate the given options:
- [tex]\( k - 6 \)[/tex]: This represents subtracting 6 from [tex]\( k \)[/tex], which is not the product of [tex]\( k \)[/tex] and 6.
- [tex]\( 6 k \)[/tex]: This represents multiplying [tex]\( k \)[/tex] by 6, which correctly translates the phrase.
- [tex]\( k + 6 \)[/tex]: This represents adding 6 to [tex]\( k \)[/tex], which is not the product of [tex]\( k \)[/tex] and 6.
- [tex]\( \frac{k}{6} \)[/tex]: This represents dividing [tex]\( k \)[/tex] by 6, which is not the product of [tex]\( k \)[/tex] and 6.
Given the correct interpretation, the algebraic expression for "the product of [tex]\( k \)[/tex] and 6" is:
[tex]\[ 6 k \][/tex]
