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. 0

D. [tex]\(\frac{1}{2}\)[/tex]

Let's solve the equation step-by-step:

The equation given in Karissa's work is:

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

Step 1: Expand both sides of the equation.

On the left side:

[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]

This simplifies to:

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

On the right side:

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

This simplifies to:

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

So, we now have the equation:

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

Step 2: Subtract 4 from both sides.

This gives us:

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

Step 3: 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]

Simplifying the left side:

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

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