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Answer :
To find the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through the steps to solve it:
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute and simplify both sides:
Left side: [tex]\(\frac{1}{2}(x - 14) = \frac{1}{2}x - 7\)[/tex]
Adding 11 gives: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]
This simplifies to: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex]
3. Set the simplified left side equal to the simplified right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides to focus on the variable terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate the variable [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
The value of [tex]\( x \)[/tex] that satisfies the original equation is [tex]\( \boxed{0} \)[/tex].
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute and simplify both sides:
Left side: [tex]\(\frac{1}{2}(x - 14) = \frac{1}{2}x - 7\)[/tex]
Adding 11 gives: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]
This simplifies to: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex]
3. Set the simplified left side equal to the simplified right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides to focus on the variable terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate the variable [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
The value of [tex]\( x \)[/tex] that satisfies the original equation is [tex]\( \boxed{0} \)[/tex].
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