Answer :
Let's solve the equation step-by-step:
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Simplify both sides:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Calculate [tex]\(\frac{1}{2} \times 14\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Now, simplify both sides:
3. Simplify the left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
4. Simplify the right side:
[tex]\[
\frac{1}{2}x - x + 4 \Rightarrow -\frac{1}{2}x + 4
\][/tex]
We now have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To solve for [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Simplify both sides:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Calculate [tex]\(\frac{1}{2} \times 14\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Now, simplify both sides:
3. Simplify the left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
4. Simplify the right side:
[tex]\[
\frac{1}{2}x - x + 4 \Rightarrow -\frac{1}{2}x + 4
\][/tex]
We now have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To solve for [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].