Answer :
We start with the equation
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4).
$$[/tex]
Step 1. Expand both sides:
On the left side:
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
On the right side:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Now the equation becomes
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Subtract 4 from both sides to isolate the terms with [tex]$x$[/tex]:
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$[/tex]
which simplifies to
[tex]$$
\frac{1}{2} x = -\frac{1}{2} x.
$$[/tex]
Step 3. Add [tex]$\frac{1}{2} x$[/tex] to both sides to combine like terms:
[tex]$$
\frac{1}{2} x + \frac{1}{2} x = -\frac{1}{2} x + \frac{1}{2} x,
$$[/tex]
which simplifies to
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$0$[/tex].
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4).
$$[/tex]
Step 1. Expand both sides:
On the left side:
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
On the right side:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Now the equation becomes
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Subtract 4 from both sides to isolate the terms with [tex]$x$[/tex]:
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$[/tex]
which simplifies to
[tex]$$
\frac{1}{2} x = -\frac{1}{2} x.
$$[/tex]
Step 3. Add [tex]$\frac{1}{2} x$[/tex] to both sides to combine like terms:
[tex]$$
\frac{1}{2} x + \frac{1}{2} x = -\frac{1}{2} x + \frac{1}{2} x,
$$[/tex]
which simplifies to
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$0$[/tex].