Karissa begins to solve 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]

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]

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

The original equation is:

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

1. Distribute the fractions and simplify both sides:

Left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]

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

2. Equate the simplified expressions:

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

3. Subtract 4 from both sides:

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

4. Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine like terms:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

[tex]\[
x = 0
\][/tex]

So, the value of [tex]$x$[/tex] is [tex]$0$[/tex].