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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 go through the solution step by step:
1. Distribute and simplify both sides:
Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] to [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine like terms:
On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Eliminate terms to solve for [tex]\(x\)[/tex]:
Subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To eliminate the variable on the right side, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine the terms on the left side:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation is [tex]\(x = 0\)[/tex].
1. Distribute and simplify both sides:
Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] to [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine like terms:
On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Eliminate terms to solve for [tex]\(x\)[/tex]:
Subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To eliminate the variable on the right side, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine the terms on the left side:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation is [tex]\(x = 0\)[/tex].
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