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

1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]

2. Distribute the [tex]$\frac{1}{2}$[/tex] on both sides:
- Left side: [tex]$\frac{1}{2}(x) - \frac{1}{2}(14) + 11 = \frac{1}{2}x - 7 + 11$[/tex]
- Right side: [tex]$\frac{1}{2}x - x + 4$[/tex]

3. Simplify both sides:
- Left side becomes: [tex]$\frac{1}{2}x + 4$[/tex]
- Right side becomes: [tex]$-\frac{1}{2}x + 4$[/tex]

4. Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

5. Subtract 4 from both sides to eliminate the constants:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

6. Add [tex]$\frac{1}{2}x$[/tex] to both sides to isolate [tex]$x$[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]

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