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

Sure, let's solve the equation step-by-step to find the value of [tex]$ x $[/tex].

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

Step 1: Distribute the [tex]$\frac{1}{2}$[/tex] on the left side:
[tex]\[
\frac{1}{2} \times (x - 14) + 11 = \frac{1}{2}x - \left(x - 4\right)
\][/tex]

This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

Step 2: Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]

Step 3: Combine like terms. On the right side, the terms [tex]$\frac{1}{2}x - x$[/tex] simplify to:
[tex]\[
-\frac{1}{2}x
\][/tex]

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

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

Step 5: Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine the [tex]$x$[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]

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

So, the value of [tex]$ x $[/tex] that satisfies the equation is [tex]$ \boxed{0} $[/tex].