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 go through the steps one by one:

1. Expand and Simplify Both Sides:

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

- Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2}(14) + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Simplify [tex]\(\frac{1}{2}(14)\)[/tex] to get 7:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Combine constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]

2. Subtract 4 from Both Sides:

Next, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

3. Add [tex]\(\frac{1}{2}x\)[/tex] to Both Sides:

To isolate [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]

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

After following these steps, we find that the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].