Answer :
We start with the equation
[tex]$$
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4).
$$[/tex]
1. Distribute and simplify each side:
On the left, distribute the [tex]$\frac{1}{2}$[/tex] over [tex]$(x-14)$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{1}{2}\cdot14=\frac{1}{2}x-7.
$$[/tex]
Then, add [tex]$11$[/tex] to obtain:
[tex]$$
\frac{1}{2}x-7+11 = \frac{1}{2}x+4.
$$[/tex]
On the right, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4.
$$[/tex]
Simplify the [tex]$\frac{1}{2}x - x$[/tex] by writing [tex]$x$[/tex] as [tex]$\frac{2}{2}x$[/tex]:
[tex]$$
\frac{1}{2}x - \frac{2}{2}x = -\frac{1}{2}x,
$$[/tex]
so the right side becomes:
[tex]$$
-\frac{1}{2}x + 4.
$$[/tex]
2. Write the simpler equation:
The equation now is:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]
3. Subtract [tex]$4$[/tex] from both sides:
Eliminating the constant term, we subtract [tex]$4$[/tex]:
[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]
4. Combine like terms:
Add [tex]$\frac{1}{2}x$[/tex] to both sides to bring like terms together:
[tex]$$
\frac{1}{2}x+\frac{1}{2}x = 0.
$$[/tex]
The left side becomes:
[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]
1. Distribute and simplify each side:
On the left, distribute the [tex]$\frac{1}{2}$[/tex] over [tex]$(x-14)$[/tex]:
[tex]$$
\frac{1}{2}(x-14)=\frac{1}{2}x-\frac{1}{2}\cdot14=\frac{1}{2}x-7.
$$[/tex]
Then, add [tex]$11$[/tex] to obtain:
[tex]$$
\frac{1}{2}x-7+11 = \frac{1}{2}x+4.
$$[/tex]
On the right, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4.
$$[/tex]
Simplify the [tex]$\frac{1}{2}x - x$[/tex] by writing [tex]$x$[/tex] as [tex]$\frac{2}{2}x$[/tex]:
[tex]$$
\frac{1}{2}x - \frac{2}{2}x = -\frac{1}{2}x,
$$[/tex]
so the right side becomes:
[tex]$$
-\frac{1}{2}x + 4.
$$[/tex]
2. Write the simpler equation:
The equation now is:
[tex]$$
\frac{1}{2}x+4=-\frac{1}{2}x+4.
$$[/tex]
3. Subtract [tex]$4$[/tex] from both sides:
Eliminating the constant term, we subtract [tex]$4$[/tex]:
[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]
4. Combine like terms:
Add [tex]$\frac{1}{2}x$[/tex] to both sides to bring like terms together:
[tex]$$
\frac{1}{2}x+\frac{1}{2}x = 0.
$$[/tex]
The left side becomes:
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is
[tex]$$
\boxed{0}.
$$[/tex]
