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

Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex]:

The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

Step 1: Distribute and simplify both sides.
- On the left-hand side, distribute [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

- On the right-hand side, distribute and simplify:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

Step 2: Equate the simplified expressions from both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Step 3: Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Step 4: Move all [tex]\( x \)[/tex] terms to one side:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Step 5: Combine the [tex]\( x \)[/tex] terms:
[tex]\[
x = 0
\][/tex]

Thus, the value of [tex]\( x \)[/tex] that satisfies the equation is:
[tex]\[
\boxed{0}
\][/tex]