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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
Expand the left-hand side:
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
Expand the right-hand side:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
So the equation becomes
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Eliminate the constant
Subtract [tex]$4$[/tex] from both sides:
[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. Solve for [tex]$x$[/tex]
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]
This gives
[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
Expand the left-hand side:
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
Expand the right-hand side:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
So the equation becomes
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Eliminate the constant
Subtract [tex]$4$[/tex] from both sides:
[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. Solve for [tex]$x$[/tex]
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]
This gives
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].
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