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, the equation [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], follow these steps based on Karissa's work:

1. Distribute terms:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(-14\)[/tex]:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]

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

2. Simplify both sides:
- Combine like terms on the left:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]

- The right side simplifies to:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]

3. Resulting equation:
- After simplification, both sides are:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

4. Isolate the variable [tex]\(x\)[/tex]:
- Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

5. Solve for [tex]\(x\)[/tex]:
- To eliminate the fractions, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

- Combine the terms on the left:
[tex]\[
x = 0
\][/tex]

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