To determine which algebraic expression represents the phrase "two times the quantity of a number minus 12," let's break down the phrase step by step.
1. Identify the number: Let's denote the unknown number by [tex]\( y \)[/tex].
2. Subtract 12 from the number: This operation will give us [tex]\( y - 12 \)[/tex].
3. Take two times this quantity: We need to multiply the expression [tex]\( y - 12 \)[/tex] by 2.
Putting it all together, we get:
[tex]\[ 2 \times (y - 12) \][/tex]
This is mathematically written as:
[tex]\[ 2(y - 12) \][/tex]
Now, examine the given options:
1. [tex]\( 2y - 12 \)[/tex]
2. [tex]\( 2(y - 12) \)[/tex]
3. [tex]\( 2(y + 12) \)[/tex]
4. [tex]\( 2y + 12 \)[/tex]
The correct algebraic expression that represents "two times the quantity of a number minus 12" is:
[tex]\[ 2(y - 12) \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{2(y-12)} \][/tex]
