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. 0
C. 1

Sure! Let's solve the equation step-by-step based on Karissa's work:

1. Original Equation:
[tex]$\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)$[/tex]

2. Distribute and Simplify the Left Side:
[tex]$\frac{1}{2} \times (x-14) = \frac{1}{2}x - 7$[/tex]
So, the left side becomes:
[tex]$\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4$[/tex]

3. Simplify the Right Side:
Distribute the negative sign:
[tex]$\frac{1}{2}x - x + 4$[/tex]

4. Equations After Distribution:
So, the equation now looks like this:
[tex]$\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4$[/tex]

5. Further Simplify Both Sides:
The left side stays: [tex]$\frac{1}{2}x + 4$[/tex]
The right side simplifies to: [tex]$-\frac{1}{2}x + 4$[/tex]

6. Equate and Solve for [tex]$x$[/tex]:
Set up the equation:
[tex]$\frac{1}{2}x + 4 = -\frac{1}{2}x + 4$[/tex]

7. Subtract 4 from Both Sides:
[tex]$\frac{1}{2}x = -\frac{1}{2}x$[/tex]

8. Combine Like 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]
[tex]$x = 0$[/tex]

The value of [tex]$x$[/tex] is [tex]$0$[/tex].