Karissa begins to solve the equation:

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

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, $\frac{1}{2}x = -\frac{1}{2}x$ results. What is the value of $x$?

A. $-1$

B. $-\frac{1}{2}$

C. 0

D. $\frac{1}{2}$

Sure! Let's solve the given equation step-by-step.

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

First, let's distribute and simplify both sides of the equation.

Step 1: Distribute terms inside the parentheses.
[tex]\[ \frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4) \][/tex]
This simplifies to:
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]

Step 2: Combine like terms on both sides.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
Simplify the left side:
[tex]\[ \frac{1}{2}x + 4 = \][/tex]
Simplify the right side:
[tex]\[ \frac{1}{2}x - x + 4 \][/tex]
This gives:
[tex]\[ \frac{1}{2}x + 4 = -\frac{1}{2}x + 4 \][/tex]

Step 3: Subtract 4 from both sides to further simplify.
[tex]\[ \frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \][/tex]
This results in:
[tex]\[ \frac{1}{2}x = -\frac{1}{2}x \][/tex]

Step 4: Add [tex]$\frac{1}{2}x$[/tex] to both sides to isolate [tex]$x$[/tex].
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \][/tex]
This simplifies to:
[tex]\[ x = 0 \][/tex]

So, the value of [tex]$x$[/tex] that satisfies the equation is:
[tex]\[ \boxed{0} \][/tex]

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