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Answer :
Sure! Let's go through the steps to solve the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x - 4)\)[/tex] step-by-step.
1. Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] to both terms inside the parentheses on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
Simplifying the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
3. Combine like terms on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x - 4)
\][/tex]
4. Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
5. Combine like terms on the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
6. Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
Simplifying both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
7. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying further:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
Thus, the correct answer is:
```
0
```
1. Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] to both terms inside the parentheses on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
Simplifying the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
3. Combine like terms on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x - 4)
\][/tex]
4. Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
5. Combine like terms on the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
6. Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
Simplifying both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
7. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying further:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
Thus, the correct answer is:
```
0
```
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