To determine 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 Unknown Number:
- Let the unknown number be represented by [tex]\( x \)[/tex].
2. Half of a Number:
- To find half of the number [tex]\( x \)[/tex], we use the expression [tex]\( \frac{1}{2}x \)[/tex].
3. Seven More Than:
- When we say "seven more than" a quantity, we mean we add 7 to that quantity.
Combining these steps, "seven more than half of a number" can be written algebraically as:
[tex]\[ \frac{1}{2}x + 7 \][/tex]
Now, let's compare this with the provided options:
1. [tex]\( 7 - \frac{1}{2} x \)[/tex]
2. [tex]\( -7 + \frac{1}{2} x \)[/tex]
3. [tex]\( \frac{1}{2} x + 7 \)[/tex]
4. [tex]\( -\frac{1}{2} x - 7 \)[/tex]
Among these options, the expression [tex]\( \frac{1}{2} x + 7 \)[/tex] correctly represents the phrase "seven more than half of a number."
Therefore, the correct option is:
[tex]\[ \boxed{3} \][/tex]
