Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
We start with the following equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute [tex]\(\frac{1}{2}\)[/tex] into [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
- On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine like terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So, we now have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract [tex]\(4\)[/tex] from both sides:
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine like terms:
[tex]\[
x = 0
\][/tex]
The value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
We start with the following equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute [tex]\(\frac{1}{2}\)[/tex] into [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
- On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine like terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So, we now have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract [tex]\(4\)[/tex] from both sides:
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine like terms:
[tex]\[
x = 0
\][/tex]
The value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
