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. 0
D. [tex]$\frac{1}{2}$[/tex]

Sure! Let’s solve the equation step-by-step to find the value of [tex]$ x $[/tex].

The equation given is:

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

Step 1: Distribute the [tex]$\frac{1}{2}$[/tex] on the left side.

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

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

Step 2: Simplify both sides.

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

Step 3: Move the constant on both sides by subtracting 4 from each side.

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

Step 4: Simplify the right side by combining like terms.

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

Step 5: To solve this, add [tex]$\frac{1}{2}x$[/tex] to both sides to get:

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

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

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