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Answer :
We start with the original equation:
[tex]$$
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4).
$$[/tex]
Step 1. Expand both sides:
- On the left, 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 [tex]$11$[/tex]:
[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]
Notice that [tex]$\frac{1}{2} x - x$[/tex] simplifies to:
[tex]$$
\frac{1}{2} x - x = -\frac{1}{2}x.
$$[/tex]
So the right side becomes:
[tex]$$
-\frac{1}{2} x + 4.
$$[/tex]
Step 2. Write the simplified equation:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 3. Eliminate the constant term by subtracting [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]
Step 4. Solve for [tex]$x$[/tex]:
Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine like terms:
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = 0,
$$[/tex]
which simplifies to:
[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 both sides:
- On the left, 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 [tex]$11$[/tex]:
[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]
Notice that [tex]$\frac{1}{2} x - x$[/tex] simplifies to:
[tex]$$
\frac{1}{2} x - x = -\frac{1}{2}x.
$$[/tex]
So the right side becomes:
[tex]$$
-\frac{1}{2} x + 4.
$$[/tex]
Step 2. Write the simplified equation:
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 3. Eliminate the constant term by subtracting [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]
Step 4. Solve for [tex]$x$[/tex]:
Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine like terms:
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = 0,
$$[/tex]
which simplifies to:
[tex]$$
x = 0.
$$[/tex]
Thus, the value of [tex]$x$[/tex] is [tex]$\boxed{0}$[/tex].
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Rewritten by : Barada
