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. 0

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

To solve the equation step-by-step, let's go through the process that Karissa followed:

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 the left side, and simplify the right side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

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

5. Combine like terms:
[tex]\[
x = 0
\][/tex]

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