Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
We're starting with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute and simplify:
Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplify it:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
Distribute the minus sign on the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
2. Set the simplified forms equal:
Now we have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Eliminate [tex]\(-\frac{1}{2}x\)[/tex] from the right side by adding it to both sides:
Adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
We're starting with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute and simplify:
Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplify it:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
Distribute the minus sign on the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
2. Set the simplified forms equal:
Now we have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Eliminate [tex]\(-\frac{1}{2}x\)[/tex] from the right side by adding it to both sides:
Adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
