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:

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

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. -\frac{1}{2}
C. 0
D. \frac{1}{2}

Let's solve the equation step-by-step.

The original equation given is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

Step 1: Expand and simplify both sides

- On the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]

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

The equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Step 2: Isolate the terms involving [tex]\(x\)[/tex]

Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Step 3: 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]

Combine like terms:
[tex]\[
x = 0
\][/tex]

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