Answer :
Let's solve the equation step by step:
We start with:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, expand both sides:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Now we have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To eliminate the fractions, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[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:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, expand both sides:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Now we have:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To eliminate the fractions, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[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].
