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{align}

\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{align}

\][/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. -1
B. [tex]\(\frac{1}{2}\)[/tex]
C. 0
D. 1

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

The equation starts off as:

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

1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]

2. Simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x-4)
\][/tex]

3. Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]

4. Combine like terms on the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

5. Subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

7. Simplify the left side:
[tex]\[
x = 0
\][/tex]

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