Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's work through it step by step:
1. Distribute and simplify both sides:
- Left side: [tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].
- Simplify it further to: [tex]\(\frac{1}{2}x + 4\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] simplifies to [tex]\(\frac{1}{2}x - x + 4\)[/tex].
- Simplify it to: [tex]\(-\frac{1}{2}x + 4\)[/tex].
2. Set both sides equal:
- Now, you have the equation [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex].
3. Subtract 4 from both sides:
- This gives [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
- [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
- Simplifies to: [tex]\(x = 0\)[/tex].
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute and simplify both sides:
- Left side: [tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex].
- Simplify it further to: [tex]\(\frac{1}{2}x + 4\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] simplifies to [tex]\(\frac{1}{2}x - x + 4\)[/tex].
- Simplify it to: [tex]\(-\frac{1}{2}x + 4\)[/tex].
2. Set both sides equal:
- Now, you have the equation [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex].
3. Subtract 4 from both sides:
- This gives [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
- [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
- Simplifies to: [tex]\(x = 0\)[/tex].
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
