To solve the question "Which algebraic expression represents the phrase 'seven more than half of a number'?", let's break down the phrase step by step.
1. Identify the expression for "half of a number":
- Let [tex]\( x \)[/tex] represent the number.
- Half of [tex]\( x \)[/tex] is written as [tex]\(\frac{1}{2} x\)[/tex].
2. Understand "seven more than":
- "More than" in mathematical terms means addition.
- Therefore, "seven more than" means you should add 7 to the previously identified expression.
Combining these steps together:
- The phrase "seven more than half of a number" translates to taking half of the number [tex]\(\frac{1}{2} x\)[/tex] and then adding 7 to it.
The algebraic expression for this phrase is:
[tex]\[
\frac{1}{2} x + 7
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
\frac{1}{2} x + 7
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{\frac{1}{2} x + 7}
\][/tex]
