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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 steps one by one:
1. Distribute and simplify both sides:
- Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - x + 4
\][/tex]
This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Simplify within each side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
2. Subtract 4 from both sides:
Remove the constant term on both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
Adding [tex]\(\frac{1}{2}x\)[/tex] to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
4. Combine like terms:
Combine the [tex]\(x\)[/tex] terms on the left:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute and simplify both sides:
- Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - x + 4
\][/tex]
This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
- Simplify within each side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
2. Subtract 4 from both sides:
Remove the constant term on both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
Adding [tex]\(\frac{1}{2}x\)[/tex] to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
4. Combine like terms:
Combine the [tex]\(x\)[/tex] terms on the left:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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