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Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex], we can go through each step:
1. Distribute and simplify each side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
- On the left side: Distribute [tex]\(\frac{1}{2}\)[/tex] over [tex]\(x-14\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplify it to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side: Distribute the negative sign over [tex]\(x-4\)[/tex]:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify it to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
2. Set the simplified expressions equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To solve this, add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(x\)[/tex] terms on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This becomes:
[tex]\[
x = 0
\][/tex]
The value of [tex]\(x\)[/tex] is 0.
1. Distribute and simplify each side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
- On the left side: Distribute [tex]\(\frac{1}{2}\)[/tex] over [tex]\(x-14\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplify it to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side: Distribute the negative sign over [tex]\(x-4\)[/tex]:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify it to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
2. Set the simplified expressions equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To solve this, add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(x\)[/tex] terms on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This becomes:
[tex]\[
x = 0
\][/tex]
The value of [tex]\(x\)[/tex] is 0.
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