Answer :
Let's solve the equation step-by-step to find the value of [tex]\(x\)[/tex]:
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Now, simplify the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[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 to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This gives:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Now, simplify the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[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 to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This gives:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
