Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
Starting with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides of the equation.
Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Combine like terms on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Simplify the equation further.
On the right side, simplify [tex]\(\frac{1}{2}x - x\)[/tex]:
[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]
Step 3: 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 simplifies to:
[tex]\[
x = 0
\][/tex]
Conclusion:
The value of [tex]\( x \)[/tex] is [tex]\( \boxed{0} \)[/tex].
Starting with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides of the equation.
Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Combine like terms on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Simplify the equation further.
On the right side, simplify [tex]\(\frac{1}{2}x - x\)[/tex]:
[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]
Step 3: 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 simplifies to:
[tex]\[
x = 0
\][/tex]
Conclusion:
The value of [tex]\( x \)[/tex] is [tex]\( \boxed{0} \)[/tex].
