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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 follow the steps:
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute on both sides:
- On the left side: [tex]\(\frac{1}{2}x - 7 + 11\)[/tex]
- On the right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
So we have:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
- Left side: [tex]\(\frac{1}{2}x + 4\)[/tex]
- Right side: [tex]\(-\frac{1}{2}x + 4\)[/tex]
Now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get rid of [tex]\(x\)[/tex] on the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
6. Combine the terms:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute on both sides:
- On the left side: [tex]\(\frac{1}{2}x - 7 + 11\)[/tex]
- On the right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
So we have:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
- Left side: [tex]\(\frac{1}{2}x + 4\)[/tex]
- Right side: [tex]\(-\frac{1}{2}x + 4\)[/tex]
Now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get rid of [tex]\(x\)[/tex] on the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
6. Combine the terms:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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