Answer :
We begin 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-hand side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$[/tex]
So the left-hand side becomes
[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
On the right-hand side, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Now the equation is
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2: Subtract 4 from both sides to remove the constant term:
[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]
The right-hand side becomes 0:
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4).
$$[/tex]
Step 1: Expand both sides. On the left-hand side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$[/tex]
So the left-hand side becomes
[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
On the right-hand side, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Now the equation is
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2: Subtract 4 from both sides to remove the constant term:
[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]
The right-hand side becomes 0:
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].