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]:

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

Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]

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

Combine like terms on 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]

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]

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

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