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. Expand and Simplify Both Sides:
Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
- Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2}(14) + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Simplify [tex]\(\frac{1}{2}(14)\)[/tex] to get 7:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Combine constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
2. Subtract 4 from Both Sides:
Next, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Add [tex]\(\frac{1}{2}x\)[/tex] to Both Sides:
To isolate [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
After following these steps, we find that the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Expand and Simplify Both Sides:
Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
- Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2}(14) + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Simplify [tex]\(\frac{1}{2}(14)\)[/tex] to get 7:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Combine constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
2. Subtract 4 from Both Sides:
Next, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Add [tex]\(\frac{1}{2}x\)[/tex] to Both Sides:
To isolate [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
After following these steps, we find that the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
