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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 and simplify the left side:
[tex]$$
\frac{1}{2}(x-14)+11 = \frac{1}{2}x - \frac{1}{2}(14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
Step 2. Expand and simplify the right side:
[tex]$$
\frac{1}{2}x-(x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 3. The equation now becomes:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 4. Subtract 4 from both sides to eliminate the constant:
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \quad \Longrightarrow \quad \frac{1}{2}x = -\frac{1}{2}x.
$$[/tex]
Step 5. Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine like terms:
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \quad \Longrightarrow \quad x = 0.
$$[/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 and simplify the left side:
[tex]$$
\frac{1}{2}(x-14)+11 = \frac{1}{2}x - \frac{1}{2}(14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
Step 2. Expand and simplify the right side:
[tex]$$
\frac{1}{2}x-(x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 3. The equation now becomes:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 4. Subtract 4 from both sides to eliminate the constant:
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \quad \Longrightarrow \quad \frac{1}{2}x = -\frac{1}{2}x.
$$[/tex]
Step 5. Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine like terms:
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \quad \Longrightarrow \quad x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].
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