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]

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

Step 1: Distribute and simplify

On the left side, distribute [tex]$\frac{1}{2}$[/tex] to [tex]$(x-14)$[/tex]:
[tex]$$
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11.
$$[/tex]
Combine the constant terms:
[tex]$$
\frac{1}{2}x + 4.
$$[/tex]

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

So, the equation now becomes:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]

Step 2: Isolate the variable terms

Subtract [tex]$4$[/tex] from both sides to remove the constant:
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$[/tex]
which 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 to combine like terms:
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = 0,
$$[/tex]
which gives:
[tex]$$
x = 0.
$$[/tex]

Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].