Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's carefully go through the steps:
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on both sides:
- Left side: [tex]\(\frac{1}{2}(x) - \frac{1}{2}(14) + 11 = \frac{1}{2}x - 7 + 11\)[/tex]
- Right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
3. Simplify both sides:
- Left side becomes: [tex]\(\frac{1}{2}x + 4\)[/tex]
- Right side becomes: [tex]\(-\frac{1}{2}x + 4\)[/tex]
4. Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract 4 from both sides to eliminate the constants:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation 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 the [tex]\(\frac{1}{2}\)[/tex] on both sides:
- Left side: [tex]\(\frac{1}{2}(x) - \frac{1}{2}(14) + 11 = \frac{1}{2}x - 7 + 11\)[/tex]
- Right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
3. Simplify both sides:
- Left side becomes: [tex]\(\frac{1}{2}x + 4\)[/tex]
- Right side becomes: [tex]\(-\frac{1}{2}x + 4\)[/tex]
4. Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract 4 from both sides to eliminate the constants:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
