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]

To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through Karissa's work step-by-step to find the value of [tex]\(x\)[/tex]:

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

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

3. Simplify both sides:
- On the left side: [tex]\(-7 + 11\)[/tex] simplifies to [tex]\(4\)[/tex]
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side: Combine like terms [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{1}{2}x\)[/tex]
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

4. The equation now looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

5. Subtract [tex]\(4\)[/tex] from both sides to simplify:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

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

Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].