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Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex] step-by-step, let's break it down:
1. Expand the expressions:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(-14\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides of the equation:
Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
First, subtract 4 from both sides to get:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Simplify the right side:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine like terms to solve for [tex]\(x\)[/tex]:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
1. Expand the expressions:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(-14\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides of the equation:
Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
First, subtract 4 from both sides to get:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Simplify the right side:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine like terms to solve for [tex]\(x\)[/tex]:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
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