To translate the verbal phrase "the product of 12 and [tex]\( y \)[/tex] increased by 11" into algebra, let's follow a step-by-step approach:
1. Identify the Product: The product of 12 and [tex]\( y \)[/tex] can be written as [tex]\( 12y \)[/tex].
2. Increase by 11: To increase this product by 11, we add 11 to the product. Therefore, we have [tex]\( 12y + 11 \)[/tex].
Now, let's examine each choice:
- [tex]\( 12(y + 11) \)[/tex]: This expression translates to 12 times the sum of [tex]\( y \)[/tex] and 11, which expands to [tex]\( 12y + 132 \)[/tex]. This is not the correct translation.
- [tex]\( 12y + 11 \)[/tex]: This expression matches our translation of the product of 12 and [tex]\( y \)[/tex] increased by 11.
- [tex]\( 12 + 11y \)[/tex]: This expression translates to adding 12 to 11 times [tex]\( y \)[/tex]. This is not the correct translation.
- [tex]\( 12(11y) \)[/tex]: This expression translates to 12 times 11 times [tex]\( y \)[/tex], which simplifies to [tex]\( 132y \)[/tex]. This is not the correct translation.
Therefore, the correct algebraic translation of "the product of 12 and [tex]\( y \)[/tex] increased by 11" is [tex]\( 12y + 11 \)[/tex].
The correct choice is:
[tex]\[ 12y + 11 \][/tex]
