Let's solve this problem step by step.
To find the result of substituting \( x = 2 \) into each given expression, we will evaluate each expression separately.
### First expression:
[tex]\[ \frac{1}{2} x + 4 \][/tex]
1. Substitute \( x = 2 \):
[tex]\[ \frac{1}{2} \times 2 + 4 \][/tex]
2. Simplify the multiplication:
[tex]\[ \frac{2}{2} + 4 \][/tex]
3. \(\frac{2}{2}\) simplifies to 1:
[tex]\[ 1 + 4 \][/tex]
4. Add the terms:
[tex]\[ 1 + 4 = 5 \][/tex]
So, the first expression equals 5 when \( x = 2 \).
### Second expression:
[tex]\[ x + 6 - \frac{1}{2} x - 2 \][/tex]
1. Substitute \( x = 2 \):
[tex]\[ 2 + 6 - \frac{1}{2} \times 2 - 2 \][/tex]
2. Simplify the multiplication:
[tex]\[ 2 + 6 - 1 - 2 \][/tex]
3. Combine like terms:
[tex]\[ 2 + 6 - 1 - 2 = 8 - 1 - 2 \][/tex]
4. Continue combining:
[tex]\[ 8 - 1 = 7 \][/tex]
[tex]\[ 7 - 2 = 5 \][/tex]
So, the second expression also equals 5 when \( x = 2 \).
### Conclusion
Both expressions evaluate to 5 when substituting \( x = 2 \). Therefore, the correct answer is:
Both expressions equal 5 when substituting 2 for [tex]\( x \)[/tex] because the expressions are equivalent.
