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------------------------------------------------ Which is an equivalent expression to

[tex]\[
\frac{1}{2} x + 4 \frac{1}{2} + \frac{1}{2} x - \frac{1}{2}?
\][/tex]

A. [tex]\(\frac{1}{2} x + 4 \frac{1}{2}\)[/tex]

B. [tex]\(x + 5\)[/tex]

C. [tex]\(x + 4\)[/tex]

D. [tex]\(\frac{1}{2} x - 4 \frac{1}{2}\)[/tex]

To solve the given expression and find its equivalent, let's break it down step-by-step.

We have the expression:

[tex]\[
\frac{1}{2} x + 4 \frac{1}{2} + \frac{1}{2} x - \frac{1}{2}
\][/tex]

1. Combine the like terms involving [tex]\( x \)[/tex]:

[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 1 x
\][/tex]

2. Combine the constant terms:

[tex]\[
4 \frac{1}{2} - \frac{1}{2} = 4
\][/tex]

3. Put it all together:

The simplified expression is:

[tex]\[
x + 4
\][/tex]

So, the equivalent expression is [tex]\( x + 4 \)[/tex].

From the given options, the correct choice is:

(C) [tex]\( x + 4 \)[/tex]