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Answer :
To find an equivalent expression to [tex]\(\frac{1}{2} x + 4 \frac{1}{2} + \frac{1}{2} x - \frac{1}{2}\)[/tex], let's break it down step by step.
1. Combine Like Terms:
- Start by identifying and combining the similar terms in the expression. Here, the term [tex]\(\frac{1}{2} x\)[/tex] appears twice.
- When we add them together, we have:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 1 x
\][/tex]
2. Combine Constant Numbers:
- Next, let's add the constant numbers in the expression:
- Combine [tex]\(4 \frac{1}{2}\)[/tex] and [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
4 \frac{1}{2} - \frac{1}{2} = 4
\][/tex]
3. Write the Simplified Expression:
- Now, put it all together:
- The simplified expression becomes [tex]\(x + 4\)[/tex].
Therefore, the equivalent expression to [tex]\(\frac{1}{2} x + 4 \frac{1}{2} + \frac{1}{2} x - \frac{1}{2}\)[/tex] is [tex]\(\boxed{x + 4}\)[/tex], which corresponds to option (C).
1. Combine Like Terms:
- Start by identifying and combining the similar terms in the expression. Here, the term [tex]\(\frac{1}{2} x\)[/tex] appears twice.
- When we add them together, we have:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 1 x
\][/tex]
2. Combine Constant Numbers:
- Next, let's add the constant numbers in the expression:
- Combine [tex]\(4 \frac{1}{2}\)[/tex] and [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
4 \frac{1}{2} - \frac{1}{2} = 4
\][/tex]
3. Write the Simplified Expression:
- Now, put it all together:
- The simplified expression becomes [tex]\(x + 4\)[/tex].
Therefore, the equivalent expression to [tex]\(\frac{1}{2} x + 4 \frac{1}{2} + \frac{1}{2} x - \frac{1}{2}\)[/tex] is [tex]\(\boxed{x + 4}\)[/tex], which corresponds to option (C).
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