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]
Step 1: Distribute and simplify both sides.
The left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
The right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Step 2: Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get:
[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 0.
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
The left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
The right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Step 2: Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get:
[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 0.