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Answer :
Sure, let's solve this step by step:
You start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Now, combine like terms on each side. On the left side, [tex]\(-7 + 11\)[/tex] becomes [tex]\(4\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Next, you'll notice that on the right side, [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{1}{2}x\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to solve for [tex]\(x\)[/tex]:
[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].
You start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Now, combine like terms on each side. On the left side, [tex]\(-7 + 11\)[/tex] becomes [tex]\(4\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Next, you'll notice that on the right side, [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{1}{2}x\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to solve for [tex]\(x\)[/tex]:
[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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