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, the equation [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]

To solve the equation [tex]$\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)$[/tex], let’s follow these steps:

1. Distribute and Simplify:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
Distribute the [tex]$\frac{1}{2}$[/tex] in the first term:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]

2. Combine Like Terms:
Simplify both sides of the equation:
[tex]\[
\frac{1}{2} x + 4 = \frac{1}{2} x - x + 4
\][/tex]

3. Eliminate Terms:
To solve this equation, subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]

4. Isolate x:
Add [tex]$\frac{1}{2} x$[/tex] to both sides to help isolate [tex]$x$[/tex]:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]

5. Solve for x:
Combine the x terms on the left side:
[tex]\[
x = 0
\][/tex]

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