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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. Distribute and simplify 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, distribute the negative sign:
[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 term by subtracting 4 from both sides:
Subtract 4 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]
which gives:
[tex]$$
x = 0.
$$[/tex]
Thus, the solution is:
[tex]$$
\boxed{0}.
$$[/tex]
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4).
$$[/tex]
Step 1. Distribute and simplify 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, distribute the negative sign:
[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 term by subtracting 4 from both sides:
Subtract 4 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]
which gives:
[tex]$$
x = 0.
$$[/tex]
Thus, the solution is:
[tex]$$
\boxed{0}.
$$[/tex]
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