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:

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

Step 1: Distribute and simplify both sides
- On the left side, distribute [tex]$\frac{1}{2}$[/tex] to [tex]$(x-14)$[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]

- On the right side, distribute the negative sign inside the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]

So we have:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

Step 2: Combine like terms
- On the left side, combine [tex]$-7$[/tex] and [tex]$11$[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

- On the right side, combine [tex]$\frac{1}{2}x$[/tex] and [tex]$-x$[/tex], which gives:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

So now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

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

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

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

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