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Answer :
To solve the equation and determine the value of [tex]\(x\)[/tex], let's go through the steps systematically.
Start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides
First, distribute on the left side:
[tex]\[
\frac{1}{2} \times (x - 14) = \frac{1}{2}x - 7
\][/tex]
So, the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Simplify the left side further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
The equation is now:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Cancel out terms
You notice [tex]\(4\)[/tex] is on both sides, so subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Here, [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to:
[tex]\[
\frac{1}{2}x - 2/2x = -\frac{1}{2}x
\][/tex]
The equation now is:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
Start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides
First, distribute on the left side:
[tex]\[
\frac{1}{2} \times (x - 14) = \frac{1}{2}x - 7
\][/tex]
So, the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Simplify the left side further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
The equation is now:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Cancel out terms
You notice [tex]\(4\)[/tex] is on both sides, so subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Here, [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to:
[tex]\[
\frac{1}{2}x - 2/2x = -\frac{1}{2}x
\][/tex]
The equation now is:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
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