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Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4)\)[/tex], you should follow these steps:
1. Apply the Distributive Property:
- Distribute [tex]\(\frac{1}{2}\)[/tex] in [tex]\(\frac{1}{2}(x-14)\)[/tex], resulting in [tex]\(\frac{1}{2}x - 7\)[/tex].
2. Rewrite the Equation:
- Substitute back into the equation to get: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)\)[/tex].
3. Simplify Both Sides:
- On the left side, combine [tex]\(-7 + 11\)[/tex] to get [tex]\(4\)[/tex], so it becomes [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side, distribute the negative sign, making it [tex]\(\frac{1}{2}x - x + 4\)[/tex].
4. Equating Both Sides:
- Write: [tex]\(\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4\)[/tex].
5. Subtract 4 from Both Sides:
- Resulting equation: [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
6. 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].
- Simplify: [tex]\(x = 0\)[/tex].
Thus, the value of [tex]\(x\)[/tex] is 0.
1. Apply the Distributive Property:
- Distribute [tex]\(\frac{1}{2}\)[/tex] in [tex]\(\frac{1}{2}(x-14)\)[/tex], resulting in [tex]\(\frac{1}{2}x - 7\)[/tex].
2. Rewrite the Equation:
- Substitute back into the equation to get: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)\)[/tex].
3. Simplify Both Sides:
- On the left side, combine [tex]\(-7 + 11\)[/tex] to get [tex]\(4\)[/tex], so it becomes [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side, distribute the negative sign, making it [tex]\(\frac{1}{2}x - x + 4\)[/tex].
4. Equating Both Sides:
- Write: [tex]\(\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4\)[/tex].
5. Subtract 4 from Both Sides:
- Resulting equation: [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
6. 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].
- Simplify: [tex]\(x = 0\)[/tex].
Thus, the value of [tex]\(x\)[/tex] is 0.
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