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Answer :
Certainly! Let's go through the equation step by step to find the value of [tex]\( x \)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute and simplify both sides:
- Left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- Right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Set the simplified expressions equal to each other:
[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]:
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]
Simplifying, we get:
[tex]\[
x = 0
\][/tex]
Therefore, the solution to the equation is [tex]\( x = 0 \)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute and simplify both sides:
- Left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- Right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Set the simplified expressions equal to each other:
[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]:
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]
Simplifying, we get:
[tex]\[
x = 0
\][/tex]
Therefore, the solution to the equation is [tex]\( x = 0 \)[/tex].
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