Answer :
Certainly! Let's solve the equation step by step.
We start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
On the left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Now our equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Eliminate the constant term `4` from both sides.
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]
Step 3: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine `x` terms.
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
We start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
On the left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Now our equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Eliminate the constant term `4` from both sides.
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]
Step 3: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine `x` terms.
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
