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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 the expressions.
For the left side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{1}{2}\times14=\frac{1}{2}x-7.
$$[/tex]
So, the left side becomes:
[tex]$$
\frac{1}{2}x-7+11=\frac{1}{2}x+4.
$$[/tex]
For 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]
The equation now is:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]
Step 2. Subtract 4 from both sides.
Subtract [tex]$4$[/tex] from each side to eliminate the constant:
[tex]$$
\frac{1}{2}x+4-4=-\frac{1}{2}x+4-4.
$$[/tex]
This simplifies to:
[tex]$$
\frac{1}{2}x=-\frac{1}{2}x.
$$[/tex]
Step 3. Solve for [tex]$x$[/tex].
To isolate [tex]$x$[/tex], add [tex]$\frac{1}{2}x$[/tex] to both sides:
[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 the expressions.
For the left side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{1}{2}\times14=\frac{1}{2}x-7.
$$[/tex]
So, the left side becomes:
[tex]$$
\frac{1}{2}x-7+11=\frac{1}{2}x+4.
$$[/tex]
For 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]
The equation now is:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]
Step 2. Subtract 4 from both sides.
Subtract [tex]$4$[/tex] from each side to eliminate the constant:
[tex]$$
\frac{1}{2}x+4-4=-\frac{1}{2}x+4-4.
$$[/tex]
This simplifies to:
[tex]$$
\frac{1}{2}x=-\frac{1}{2}x.
$$[/tex]
Step 3. Solve for [tex]$x$[/tex].
To isolate [tex]$x$[/tex], add [tex]$\frac{1}{2}x$[/tex] to both sides:
[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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