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------------------------------------------------ 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]

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

Karissa starts with the equation:

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

Step 1: Simplify both sides.

First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side of the equation:

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

So it simplifies to:

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

Combine like terms on both sides:

On the left side: [tex]\(-7 + 11 = 4\)[/tex], giving us:
[tex]\[
\frac{1}{2} x + 4
\][/tex]

On the right side:
[tex]\[
\frac{1}{2} x - x + 4 = -\frac{1}{2} x + 4
\][/tex]

The equation now becomes:

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

Step 2: Subtract 4 from both sides.

After subtracting 4 from both sides, the equation is:

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

Step 3: Combine all [tex]\( x \)[/tex] terms.

Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to isolate [tex]\( x \)[/tex]:

[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 [tex]\(\boxed{0}\)[/tex].