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------------------------------------------------ Karissa begins to solve the equation

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

Her work is correct and is shown below:

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

When she subtracts 4 from both sides,

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

results. What is the value of [tex]x[/tex]?

A. $-1$
B. $\frac{1}{2}$
C. $0$
D. $1$

We start with the equation
[tex]$$
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4).
$$[/tex]

Step 1: Expand both sides.

For the left side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{14}{2}=\frac{1}{2}x-7.
$$[/tex]
Then add 11:
[tex]$$
\frac{1}{2}x-7+11=\frac{1}{2}x+4.
$$[/tex]

For the right side, distribute the negative sign as well:
[tex]$$
\frac{1}{2}x-(x-4)=\frac{1}{2}x-x+4=-\frac{1}{2}x+4.
$$[/tex]

Step 2: Write the simplified equation:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]

Step 3: Remove the constant term (4) from both sides by subtracting 4:
[tex]$$
\frac{1}{2}x=-\frac{1}{2}x.
$$[/tex]

Step 4: Solve for [tex]$x$[/tex] by adding [tex]$\frac{1}{2}x$[/tex] to both sides:
[tex]$$
\frac{1}{2}x+\frac{1}{2}x=0 \quad \Longrightarrow \quad x=0.
$$[/tex]

Thus, the solution for [tex]$x$[/tex] is:
[tex]$$
\boxed{0}.
$$[/tex]