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. [tex]\(-1\)[/tex]

B. [tex]\(-\frac{1}{2}\)[/tex]

C. [tex]\(0\)[/tex]

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

To solve the given equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through the steps:

1. Distribute and Simplify Both Sides:

- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex]:

[tex]\[
\frac{1}{2} \cdot (x - 14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]

- Simplify by combining constants on the left side:

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

- On the right side, distribute the negative sign:

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

- Simplify:

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

2. Set the Simplified Expressions Equal:

- Now we have:

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

3. Subtract 4 from Both Sides:

- This eliminates the constant terms, yielding:

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

4. Combine Like Terms:

- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

- Simplify by combining like terms:

[tex]\[
x = 0
\][/tex]

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