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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, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x - 14) = \frac{1}{2}x - 7.
$$[/tex]
So the left side becomes:
[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
On the right side, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4.
$$[/tex]
Combine like terms:
[tex]$$
\frac{1}{2}x - x = -\frac{1}{2}x.
$$[/tex]
So the right side becomes:
[tex]$$
-\frac{1}{2}x + 4.
$$[/tex]
The equation now is:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Isolate the [tex]$x$[/tex]-terms.
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]$$
\frac{1}{2}x + \frac{1}{2}x = 0.
$$[/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. Distribute and simplify both sides.
On the left side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x - 14) = \frac{1}{2}x - 7.
$$[/tex]
So the left side becomes:
[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
On the right side, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4.
$$[/tex]
Combine like terms:
[tex]$$
\frac{1}{2}x - x = -\frac{1}{2}x.
$$[/tex]
So the right side becomes:
[tex]$$
-\frac{1}{2}x + 4.
$$[/tex]
The equation now is:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Isolate the [tex]$x$[/tex]-terms.
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]$$
\frac{1}{2}x + \frac{1}{2}x = 0.
$$[/tex]
This gives:
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].
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