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}{l}

\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. 0

D. [tex]$\frac{1}{2}$[/tex]

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

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

Step 1: Simplify both sides.

On the left side, distribute the [tex]$\frac{1}{2}$[/tex]:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

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

Step 2: Subtract 4 from both sides to simplify further.

[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Step 3: Combine all [tex]$ x $[/tex]-terms on one side.

Add [tex]$\frac{1}{2}x$[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This results in:
[tex]\[
x = 0
\][/tex]

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