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]

Certainly! Let's go through the steps to solve the given equation:

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

Karissa has already simplified this equation as follows:
1. Expand the left side: [tex]$ \frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7 $[/tex]

2. Expand the right side:
- First, distribute the negative sign: [tex]$ -(x-4) = -x + 4 $[/tex]
- Then: [tex]$ \frac{1}{2}x - x + 4 $[/tex]

Now the equation looks like:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

Next, she combined like terms:
- On the left side: [tex]$ -7 + 11 = 4 $[/tex] which gives us [tex]$ \frac{1}{2}x + 4 $[/tex]
- The right side simplifies as it is.

The equation is now:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Karissa subtracted 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

To solve [tex]$ \frac{1}{2}x = -\frac{1}{2}x $[/tex], we add [tex]$ \frac{1}{2}x $[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

This simplifies to:
[tex]\[
x = 0
\][/tex]

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