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Answer :
We start with the given equation:
$$
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4).
$$
**Step 1: Expand both sides.**
On the left-hand side, distribute $\frac{1}{2}$ within the parentheses:
$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$
The left-hand side becomes:
$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$
On the right-hand side, distribute the negative sign:
$$
\frac{1}{2} x - (x-4) = \frac{1}{2}x - x + 4.
$$
Combine the like terms on the right-hand side:
$$
\frac{1}{2}x - x = -\frac{1}{2}x.
$$
Thus, the right-hand side simplifies to:
$$
-\frac{1}{2}x + 4.
$$
**Step 2: Set the simplified sides equal to each other.**
We now have:
$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$
**Step 3: Eliminate the constant term on both sides.**
Subtract $4$ from both sides:
$$
\frac{1}{2}x = -\frac{1}{2}x.
$$
**Step 4: Solve for $x$.**
To eliminate the $-\frac{1}{2}x$ on the right, add $\frac{1}{2}x$ to both sides:
$$
\frac{1}{2}x + \frac{1}{2}x = 0 \quad \Longrightarrow \quad x = 0.
$$
Thus, the value of $x$ is:
$$
\boxed{0}.
$$
$$
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4).
$$
**Step 1: Expand both sides.**
On the left-hand side, distribute $\frac{1}{2}$ within the parentheses:
$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$
The left-hand side becomes:
$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$
On the right-hand side, distribute the negative sign:
$$
\frac{1}{2} x - (x-4) = \frac{1}{2}x - x + 4.
$$
Combine the like terms on the right-hand side:
$$
\frac{1}{2}x - x = -\frac{1}{2}x.
$$
Thus, the right-hand side simplifies to:
$$
-\frac{1}{2}x + 4.
$$
**Step 2: Set the simplified sides equal to each other.**
We now have:
$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$
**Step 3: Eliminate the constant term on both sides.**
Subtract $4$ from both sides:
$$
\frac{1}{2}x = -\frac{1}{2}x.
$$
**Step 4: Solve for $x$.**
To eliminate the $-\frac{1}{2}x$ on the right, add $\frac{1}{2}x$ to both sides:
$$
\frac{1}{2}x + \frac{1}{2}x = 0 \quad \Longrightarrow \quad x = 0.
$$
Thus, the value of $x$ is:
$$
\boxed{0}.
$$
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