Solve for [tex] x [/tex] in the equation:

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

Her work 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]

After subtracting 4 from both sides, the equation simplifies to:

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

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]:

The original equation is:

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

Step 1: Distribute and simplify both sides.

The left side:

[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]

Simplify:

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

The right side:

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

Simplify:

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

Step 2: Set the simplified expressions equal to each other:

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

Step 3: Subtract 4 from both sides:

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

Step 4: Add [tex]$\frac{1}{2}x$[/tex] to both sides to get:

[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 0.