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Answer :
Sure! Let's solve 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]
First, let's simplify both sides:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine like terms on both sides:
- Left side: [tex]\(-7 + 11 = 4\)[/tex], so we have [tex]\(\frac{1}{2}x + 4\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, let's simplify both sides:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine like terms on both sides:
- Left side: [tex]\(-7 + 11 = 4\)[/tex], so we have [tex]\(\frac{1}{2}x + 4\)[/tex].
- Right side: [tex]\(\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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