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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 start by simplifying both sides and solving for [tex]\(x\)[/tex]:
1. Expand and simplify both sides:
The left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
The right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
After simplifying both sides, we have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Subtract 4 from both sides to isolate [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Combine like terms:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
Which simplifies to:
[tex]\[
x = -1
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(-1\)[/tex].
1. Expand and simplify both sides:
The left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
The right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
After simplifying both sides, we have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Subtract 4 from both sides to isolate [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Combine like terms:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
Which simplifies to:
[tex]\[
x = -1
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(-1\)[/tex].
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