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]

Let's solve the equation step by step to find the value of [tex]$ x $[/tex].

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

Start by distributing and simplifying both sides:

1. Distribute [tex]$\frac{1}{2}$[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]

2. Now simplify [tex]$- (x-4)$[/tex] on the right side:
[tex]\[
-x + 4
\][/tex]

3. Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]

4. Simplify the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

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

5. Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]

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