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{align}
\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{align}
[/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 original equation is:

[tex]\[ \frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4) \][/tex]

First, we'll simplify both sides:

1. Expand [tex]\(\frac{1}{2}(x-14)\)[/tex]:
[tex]\[ \frac{1}{2} x - \frac{1}{2} \cdot 14 = \frac{1}{2} x - 7 \][/tex]

2. Simplify the expression [tex]\(- (x-4)\)[/tex]:
[tex]\[ -(x-4) = -x + 4 \][/tex]

Now substitute these into the equation:

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

3. Combine like terms on both sides:
- Left side:
[tex]\[ \frac{1}{2} x + 4 \][/tex]
- Right side:
[tex]\[ \frac{1}{2} x - x + 4 = -\frac{1}{2} x + 4 \][/tex]

Now the equation looks like this:

[tex]\[ \frac{1}{2} x + 4 = -\frac{1}{2} x + 4 \][/tex]

4. Subtract 4 from both sides to isolate terms with [tex]\( x \)[/tex]:

[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]

6. Simplify:

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

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].