Karissa begins to solve the equation:

[tex]
\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\]
[/tex]

Her work is correct and is shown below:

[tex]
\[
\begin{array}{c}
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4) \\
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \\
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\end{array}
\]
[/tex]

When she subtracts 4 from both sides, [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex] results. What is the value of [tex]\(x\)[/tex]?

A. [tex]\(-1\)[/tex]

B. [tex]\(-\frac{1}{2}\)[/tex]

C. 0

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

Let's solve the equation step by step:

We start with the equation:

[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x - 4)
\][/tex]

1. Simplify both sides:

On the left side, distribute [tex]\(\frac{1}{2}\)[/tex]:

[tex]\[
\frac{1}{2} x - 7 + 11
\][/tex]

Combine the constants:

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

On the right side, distribute the negative sign:

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

This simplifies to:

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

2. Write the simplified equation:

Now our equation looks like this:

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

3. Subtract 4 from both sides:

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

4. Solve for [tex]\(x\)[/tex]:

Add [tex]\(\frac{1}{2} x\)[/tex] to both sides:

[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]

[tex]\[
x = 0
\][/tex]

So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].