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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.
On the left-hand side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11.
$$[/tex]
Simplify by combining [tex]$-7 + 11$[/tex]:
[tex]$$
\frac{1}{2}x + 4.
$$[/tex]
For the right-hand side, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4.
$$[/tex]
Combine [tex]$\frac{1}{2}x - x$[/tex] by writing [tex]$x$[/tex] as [tex]$\frac{2}{2}x$[/tex]:
[tex]$$
\frac{1}{2}x - \frac{2}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Now the equation is:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Isolate the variable.
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]
Next, 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]
This gives:
[tex]$$
x = 0.
$$[/tex]
Final Answer: 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 both sides.
On the left-hand side, distribute [tex]$\frac{1}{2}$[/tex]:
[tex]$$
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11.
$$[/tex]
Simplify by combining [tex]$-7 + 11$[/tex]:
[tex]$$
\frac{1}{2}x + 4.
$$[/tex]
For the right-hand side, distribute the negative sign:
[tex]$$
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4.
$$[/tex]
Combine [tex]$\frac{1}{2}x - x$[/tex] by writing [tex]$x$[/tex] as [tex]$\frac{2}{2}x$[/tex]:
[tex]$$
\frac{1}{2}x - \frac{2}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Now the equation is:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 2. Isolate the variable.
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]
Next, 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]
This gives:
[tex]$$
x = 0.
$$[/tex]
Final Answer: The value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].
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