Let's break down the given English expressions and match them with the corresponding algebraic expressions step by step.
The expression "two more than the quantity of a number minus seven" can be understood as follows:
1. Start with a number [tex]\( x \)[/tex].
2. Subtract seven from this number: [tex]\( x - 7 \)[/tex].
3. Add two to the result.
We can translate these steps directly into an algebraic expression:
1. A number minus seven: [tex]\( x - 7 \)[/tex].
2. Two more than this quantity: [tex]\( (x - 7) + 2 \)[/tex].
Now let's check which among the given options represents the expression [tex]\((x - 7) + 2\)[/tex]:
- Option A: [tex]\((x - 7) + 2\)[/tex]. This matches our desired expression exactly.
- Option B: [tex]\((x + 2) - 7\)[/tex]. This does not match because it alters the order of operations, adding 2 before subtracting 7.
- Option C: [tex]\((2 + x) - 7\)[/tex]. This does not match because it starts by adding 2 to [tex]\( x \)[/tex] first.
- Option D: [tex]\(\frac{x}{7} + 2\)[/tex]. This does not match because it introduces division by 7, which wasn't part of the original expression.
Based on this detailed evaluation, the correct choice is:
A [tex]\((x - 7) + 2\)[/tex].
