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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 both sides.
For the left side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{14}{2}=\frac{1}{2}x-7.
$$[/tex]
Then add 11:
[tex]$$
\frac{1}{2}x-7+11=\frac{1}{2}x+4.
$$[/tex]
For the right side, distribute the negative sign as well:
[tex]$$
\frac{1}{2}x-(x-4)=\frac{1}{2}x-x+4=-\frac{1}{2}x+4.
$$[/tex]
Step 2: Write the simplified equation:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]
Step 3: Remove the constant term (4) from both sides by subtracting 4:
[tex]$$
\frac{1}{2}x=-\frac{1}{2}x.
$$[/tex]
Step 4: Solve for [tex]$x$[/tex] by adding [tex]$\frac{1}{2}x$[/tex] to both sides:
[tex]$$
\frac{1}{2}x+\frac{1}{2}x=0 \quad \Longrightarrow \quad x=0.
$$[/tex]
Thus, the solution for [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 both sides.
For the left side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{14}{2}=\frac{1}{2}x-7.
$$[/tex]
Then add 11:
[tex]$$
\frac{1}{2}x-7+11=\frac{1}{2}x+4.
$$[/tex]
For the right side, distribute the negative sign as well:
[tex]$$
\frac{1}{2}x-(x-4)=\frac{1}{2}x-x+4=-\frac{1}{2}x+4.
$$[/tex]
Step 2: Write the simplified equation:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]
Step 3: Remove the constant term (4) from both sides by subtracting 4:
[tex]$$
\frac{1}{2}x=-\frac{1}{2}x.
$$[/tex]
Step 4: Solve for [tex]$x$[/tex] by adding [tex]$\frac{1}{2}x$[/tex] to both sides:
[tex]$$
\frac{1}{2}x+\frac{1}{2}x=0 \quad \Longrightarrow \quad x=0.
$$[/tex]
Thus, the solution for [tex]$x$[/tex] is:
[tex]$$
\boxed{0}.
$$[/tex]
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