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Answer :
Sure! Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
The given equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides.
On the left side, distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
The equation now looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides to simplify further.
[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: Combine all [tex]\( x \)[/tex]-terms on one side.
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This results in:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
The given equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides.
On the left side, distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
The equation now looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides to simplify further.
[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: Combine all [tex]\( x \)[/tex]-terms on one side.
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This results in:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
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