Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
The original equation given is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, let's simplify both sides:
Left Side:
Distribute [tex]\(\frac{1}{2}\)[/tex] in [tex]\(\frac{1}{2}(x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
Now, adding 11:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Right Side:
Distribute the negative sign in [tex]\(-(x-4)\)[/tex]:
[tex]\[
-x + 4
\][/tex]
The equation becomes:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Simplify the right side:
[tex]\[
\frac{1}{2}x - x = -\frac{1}{2}x
\][/tex]
So the equation is now:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[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 [tex]\(\boxed{0}\)[/tex].
The original equation given is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, let's simplify both sides:
Left Side:
Distribute [tex]\(\frac{1}{2}\)[/tex] in [tex]\(\frac{1}{2}(x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
Now, adding 11:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Right Side:
Distribute the negative sign in [tex]\(-(x-4)\)[/tex]:
[tex]\[
-x + 4
\][/tex]
The equation becomes:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Simplify the right side:
[tex]\[
\frac{1}{2}x - x = -\frac{1}{2}x
\][/tex]
So the equation is now:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[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 [tex]\(\boxed{0}\)[/tex].
