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. -1
B. -\frac{1}{2}
C. 0
D. \frac{1}{2}

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

We start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]

Step 1: Distribute and simplify both sides.

- On the left side, distribute the [tex]\(\frac{1}{2}\)[/tex] inside the parentheses:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify by combining like terms:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

- On the right side, distribute the negative sign inside the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/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 to isolate terms with [tex]\(x\)[/tex].

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

Step 4: Combine like terms.

Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] term from the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Combine like terms:
[tex]\[
x = 0
\][/tex]

Thus, the solution to the equation is [tex]\(x = 0\)[/tex].