Karissa begins to solve the equation:

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

Her work 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]

To solve the equation [tex]$ \frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4) $[/tex], let's follow the steps that Karissa took:

1. Simplify both sides of the equation:

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

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

This simplifies our equation to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

2. Subtract 4 from both sides to isolate terms involving [tex]$ x $[/tex]:

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

3. Combine the [tex]$ x $[/tex]-terms:

Add [tex]$\frac{1}{2}x$[/tex] to both sides in order to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]

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