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Answer :
Let's work through the solution step-by-step to find the value of [tex]\( x \)[/tex].
1. Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Simplify both sides:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] into [tex]\( (x-14) \)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, distribute the minus sign in front of [tex]\((x-4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Now, your simplified equation looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Simplify further by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
The value of [tex]\( x \)[/tex] that solves the equation is [tex]\( 0 \)[/tex].
1. Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Simplify both sides:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] into [tex]\( (x-14) \)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, distribute the minus sign in front of [tex]\((x-4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Now, your simplified equation looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Simplify further by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
The value of [tex]\( x \)[/tex] that solves the equation is [tex]\( 0 \)[/tex].
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