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. -1

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

C. 0

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

To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through the solution step-by-step:

1. Distribute and Simplify Both Sides:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] through [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
- Simplifying gives:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

- On the right side, simplify the expression [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]

2. Set the Simplified Expressions Equal:
- Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

3. Eliminate the Constant Term:
- 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 to eliminate the [tex]\(x\)[/tex] term on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

- This simplifies to:
[tex]\[
x = 0
\][/tex]

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