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Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex], let's break it down step by step:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \cdot 14 = \frac{1}{2}x - 7
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Simplify the left side:
[tex]\[
-7 + 11 = 4
\][/tex]
So the left side is now:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
3. Distribute the negative sign on the right side:
[tex]\[
-(x-4) = -x + 4
\][/tex]
So the right side becomes:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
4. Combine terms on the right side:
[tex]\[
\frac{1}{2}x - x = -\frac{1}{2}x
\][/tex]
So the right side simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
5. Equating both sides:
Now, our equation looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
6. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
7. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \cdot 14 = \frac{1}{2}x - 7
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Simplify the left side:
[tex]\[
-7 + 11 = 4
\][/tex]
So the left side is now:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
3. Distribute the negative sign on the right side:
[tex]\[
-(x-4) = -x + 4
\][/tex]
So the right side becomes:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
4. Combine terms on the right side:
[tex]\[
\frac{1}{2}x - x = -\frac{1}{2}x
\][/tex]
So the right side simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
5. Equating both sides:
Now, our equation looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
6. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
7. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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