Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through the steps:
1. Begin with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]
3. Simplify both sides:
[tex]\[
\frac{1}{2} x + 4 = \frac{1}{2} x - x + 4
\][/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 isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]
6. Combine like terms on the left side:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Begin with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]
3. Simplify both sides:
[tex]\[
\frac{1}{2} x + 4 = \frac{1}{2} x - x + 4
\][/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 isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]
6. Combine like terms on the left side:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
