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. [tex]$-1$[/tex]
B. [tex]$-\frac{1}{2}$[/tex]
C. [tex]$0$[/tex]
D. [tex]$\frac{1}{2}$[/tex]

We begin with the equation

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

Step 1: Expand both sides. On the left-hand side, distribute [tex]$\frac{1}{2}$[/tex]:

[tex]$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$[/tex]

So the left-hand side becomes

[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]

On the right-hand side, distribute the negative sign:

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

Now the equation is

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

Step 2: Subtract 4 from both sides to remove the constant term:

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

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

The right-hand side becomes 0:

[tex]$$
x = 0.
$$[/tex]

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