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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 carefully follow the steps taken by Karissa:
1. Expand both sides of the equation:
- The left side: [tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].
- The right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] simplifies to [tex]\(\frac{1}{2}x - x + 4\)[/tex].
2. Simplify both sides:
- The left side: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex].
- The right side: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex].
3. Equating the simplified expressions:
- Now, the equation [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex] results.
4. Subtract 4 from both sides:
- Doing this, we get: [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
5. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms: [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
- This simplifies to [tex]\(x = 0\)[/tex].
Therefore, the value of [tex]\(x\)[/tex] is 0.
1. Expand both sides of the equation:
- The left side: [tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].
- The right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] simplifies to [tex]\(\frac{1}{2}x - x + 4\)[/tex].
2. Simplify both sides:
- The left side: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex].
- The right side: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex].
3. Equating the simplified expressions:
- Now, the equation [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex] results.
4. Subtract 4 from both sides:
- Doing this, we get: [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
5. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms: [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
- This simplifies to [tex]\(x = 0\)[/tex].
Therefore, the value of [tex]\(x\)[/tex] is 0.
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