To translate the phrase "two times the quantity of a number minus 12" into an algebraic expression, let's break down the phrase step-by-step:
1. Identify the number in question:
- Let's denote the number with the variable [tex]\( y \)[/tex].
2. Quantity of a number minus 12:
- The phrase "the quantity of a number minus 12" translates to [tex]\( y - 12 \)[/tex]. This indicates we are taking the number [tex]\( y \)[/tex] and subtracting 12 from it.
3. Two times the quantity:
- The phrase "two times the quantity" means we are doubling the entire expression [tex]\( y - 12 \)[/tex]. In algebra, "two times" an expression is written as multiplying the entire expression by 2.
Combining these steps, the translation of the entire phrase "two times the quantity of a number minus 12" results in the algebraic expression:
[tex]\[ 2(y - 12) \][/tex]
Among the given options:
- [tex]\(2 y - 12\)[/tex]
- [tex]\(2(y-12)\)[/tex]
- [tex]\(2(y+12)\)[/tex]
- [tex]\(2 y + 12\)[/tex]
The correct expression is [tex]\( 2(y - 12) \)[/tex]. This choice accurately represents the phrase as it correctly multiplies the entire quantity [tex]\((y - 12)\)[/tex] by 2. Therefore, the correct option is the second one:
[tex]\[ 2(y - 12) \][/tex]
