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Answer :
Sure! Let's solve the equation step-by-step.
The equation starts off as:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x-4)
\][/tex]
3. Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
4. Combine like terms on the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
7. Simplify the left side:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The equation starts off as:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x-4)
\][/tex]
3. Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
4. Combine like terms on the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
7. Simplify the left side:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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