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 one by one:
1. Distribute and simplify both sides:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] into [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2} x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2} x + 4
\][/tex]
- On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2} x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2} x + 4
\][/tex]
2. Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2} x + 4 = -\frac{1}{2} x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]
4. 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]
5. Combine like terms on the left side:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute and simplify both sides:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] into [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2} x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2} x + 4
\][/tex]
- On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2} x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2} x + 4
\][/tex]
2. Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2} x + 4 = -\frac{1}{2} x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]
4. 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]
5. Combine like terms on the left side:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
