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]

Sure! Let's solve the equation step-by-step.

We start with the equation:

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

First, distribute the [tex]$\frac{1}{2}$[/tex] on the left side:

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

This simplifies to:

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

Next, combine like terms:

On the left side:

[tex]\[
-7 + 11 = 4
\][/tex]

So, the equation becomes:

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

Now, get rid of the constant [tex]$4$[/tex] on both sides by subtracting [tex]$4$[/tex]:

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

Simplify the right side:

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

This gives us:

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

Now, add [tex]$\frac{1}{2}x$[/tex] to both sides to eliminate the variable on one side:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Combine the terms:

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

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