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