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]

Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].

Starting from Karissa's work:

1. The original equation is:

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

2. Distribute and simplify both sides:

- Left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].

- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex].

So now we have:

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

3. Combine like terms:

- Left side: [tex]\(-7 + 11\)[/tex] simplifies to [tex]\(4\)[/tex], so the equation is [tex]\(\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4\)[/tex].

- Right side: [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{1}{2}x\)[/tex].

So it becomes:

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

4. Subtract [tex]\(4\)[/tex] from both sides:

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

5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right side:

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

Simplifying gives:

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

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