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, 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. 0

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

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

1. Distribute and Simplify:
- Start with [tex]$\frac{1}{2}(x-14)+11$[/tex] on the left side. Distribute the [tex]$\frac{1}{2}$[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- So the expression becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- Combine the constants [tex]$-7$[/tex] and [tex]$11$[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

2. Simplify the Right Side:
- The expression is [tex]$\frac{1}{2}x - (x-4)$[/tex]. Distribute the negative sign through the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Combine [tex]$\frac{1}{2}x - x$[/tex] to simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

3. Equate and Solve:
- Now, set the two sides equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

4. Subtract 4 from Both Sides:
- This results in:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

5. Solve for [tex]$x$[/tex]:
- Add [tex]$\frac{1}{2}x$[/tex] to both sides to get:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- Simplify the left side:
[tex]\[
x = 0
\][/tex]

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