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Answer :
We begin with the equation
$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4).
$$
**Step 1. Distribute and Simplify Both Sides**
On the left side, distribute $\frac{1}{2}$:
$$
\frac{1}{2}x - \frac{1}{2}\cdot14 + 11 = \frac{1}{2}x - 7 + 11.
$$
Simplify by combining like terms:
$$
\frac{1}{2}x + 4.
$$
On the right side, distribute the negative sign:
$$
\frac{1}{2}x - x + 4.
$$
Notice that $\frac{1}{2}x - x$ can be combined:
$$
\frac{1}{2}x - x = -\frac{1}{2}x.
$$
Thus, the right side simplifies to:
$$
-\frac{1}{2}x + 4.
$$
Now our equation is:
$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$
**Step 2. Eliminate the Constant Terms**
Subtract $4$ from both sides to remove the constant:
$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$
which simplifies to:
$$
\frac{1}{2}x = -\frac{1}{2}x.
$$
**Step 3. Solve for $x$**
To eliminate the negative coefficient, add $\frac{1}{2}x$ to both sides:
$$
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x.
$$
This gives:
$$
x = 0.
$$
Thus, the value of $x$ is $\boxed{0}$.
$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4).
$$
**Step 1. Distribute and Simplify Both Sides**
On the left side, distribute $\frac{1}{2}$:
$$
\frac{1}{2}x - \frac{1}{2}\cdot14 + 11 = \frac{1}{2}x - 7 + 11.
$$
Simplify by combining like terms:
$$
\frac{1}{2}x + 4.
$$
On the right side, distribute the negative sign:
$$
\frac{1}{2}x - x + 4.
$$
Notice that $\frac{1}{2}x - x$ can be combined:
$$
\frac{1}{2}x - x = -\frac{1}{2}x.
$$
Thus, the right side simplifies to:
$$
-\frac{1}{2}x + 4.
$$
Now our equation is:
$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$
**Step 2. Eliminate the Constant Terms**
Subtract $4$ from both sides to remove the constant:
$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$
which simplifies to:
$$
\frac{1}{2}x = -\frac{1}{2}x.
$$
**Step 3. Solve for $x$**
To eliminate the negative coefficient, add $\frac{1}{2}x$ to both sides:
$$
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x.
$$
This gives:
$$
x = 0.
$$
Thus, the value of $x$ is $\boxed{0}$.
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