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Answer :
To find the value of [tex]\( x \)[/tex] in the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex], let's go through the steps that Karissa followed:
1. Distribute and Simplify:
- Left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] simplifies to [tex]\(\frac{1}{2}x - x + 4\)[/tex].
2. Combine Like Terms:
- Left side: [tex]\(\frac{1}{2}x - 7 + 11\)[/tex] simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex] becomes [tex]\(-\frac{1}{2}x + 4\)[/tex].
3. Set the Simplified Equation:
- Now, the equation is [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex].
4. Subtract 4 from Both Sides:
- This results in [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
5. Add [tex]\(\frac{1}{2}x\)[/tex] to Both Sides:
- [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
6. Simplify:
- Combining the terms gives us [tex]\(x = 0\)[/tex].
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
1. Distribute and Simplify:
- Left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] simplifies to [tex]\(\frac{1}{2}x - x + 4\)[/tex].
2. Combine Like Terms:
- Left side: [tex]\(\frac{1}{2}x - 7 + 11\)[/tex] simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex] becomes [tex]\(-\frac{1}{2}x + 4\)[/tex].
3. Set the Simplified Equation:
- Now, the equation is [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex].
4. Subtract 4 from Both Sides:
- This results in [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
5. Add [tex]\(\frac{1}{2}x\)[/tex] to Both Sides:
- [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
6. Simplify:
- Combining the terms gives us [tex]\(x = 0\)[/tex].
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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