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Answer :
Let's solve the equation step-by-step to find the value of [tex]\(x\)[/tex].
The original equation provided is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, simplify both sides of the equation.
Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the subtraction:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Which simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So, we have the equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Next, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The original equation provided is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, simplify both sides of the equation.
Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the subtraction:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Which simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So, we have the equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Next, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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