Carissa begins to solve the equation:

[tex]\[

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

\][/tex]

Her work 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, the equation [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]

We start with the equation

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

Step 1: Simplify the left side.

Distribute [tex]$\frac{1}{2}$[/tex] in the left expression:

[tex]$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$[/tex]

Then add the 11:

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

Step 2: Simplify the right side.

Distribute the negative sign on the right expression:

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

Combine like terms for [tex]$x$[/tex]:

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

so the right side becomes

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

Step 3: Set up the simplified equation.

Now the equation is

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

Step 4: Subtract 4 from both sides to eliminate the constant term.

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

which simplifies to

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

Step 5: Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine the terms containing [tex]$x$[/tex].

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

simplifying to

[tex]$$
x = 0.
$$[/tex]

Thus, the solution for [tex]$x$[/tex] is

[tex]$$
\boxed{0}.
$$[/tex]