Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. To eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
6. Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
Therefore, the answer is [tex]\( \boxed{0} \)[/tex].
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. To eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
6. Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
Therefore, the answer is [tex]\( \boxed{0} \)[/tex].
