Answer :
Let's work through the problem step by step to solve for [tex]\( x \)[/tex]:
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
First, distribute the fractions and simplify both sides of the equation:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Combine the constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Next, simplify the right side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, subtract 4 from both sides to isolate the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Now, add [tex]\( \frac{1}{2}x \)[/tex] to both sides to gather all [tex]\( x \)[/tex] terms on the left side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{0}
\][/tex]
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
First, distribute the fractions and simplify both sides of the equation:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Combine the constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Next, simplify the right side by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, subtract 4 from both sides to isolate the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Now, add [tex]\( \frac{1}{2}x \)[/tex] to both sides to gather all [tex]\( x \)[/tex] terms on the left side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{0}
\][/tex]
