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:

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

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]

Let's solve the equation step by step to find the value of [tex]$ x $[/tex]:

1. Start with the equation:

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

2. Distribute the [tex]$\frac{1}{2}$[/tex] on the left side:

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

Simplifying, we get:

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

3. Simplify both sides:

On the left side:

[tex]\[
-7 + 11 = 4
\][/tex]

So, the left side becomes:

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

On the right side:

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

Therefore, the right side becomes:

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

4. Now, the equation is:

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

5. Subtract 4 from both sides:

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

6. Combine all [tex]$ x $[/tex] terms on one side by adding [tex]$\frac{1}{2}x$[/tex] to both sides:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Simplifying, we get:

[tex]\[
x = 0
\][/tex]

So, the value of [tex]$ x $[/tex] is [tex]$ 0 $[/tex].