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Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's follow these steps:
1. Simplify Both Sides:
Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Expand and Simplify:
On the left side multiply [tex]\(\frac{1}{2}\)[/tex] with both [tex]\(x\)[/tex] and [tex]\(-14\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Combine the constants [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
3. Combine Like Terms:
The right side simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
4. Equate and Simplify Further:
Set the simplified left side equal to the simplified right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine the terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
1. Simplify Both Sides:
Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Expand and Simplify:
On the left side multiply [tex]\(\frac{1}{2}\)[/tex] with both [tex]\(x\)[/tex] and [tex]\(-14\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Combine the constants [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
3. Combine Like Terms:
The right side simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
4. Equate and Simplify Further:
Set the simplified left side equal to the simplified right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine the terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
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