Option C:
x = 0
Solution:
Given equation : [tex]\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)[/tex]
To find the value of x from the given equation.
[tex]$\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)[/tex]
[tex]$\Rightarrow\frac{1}{2}x-7+11=\frac{1}{2} x-x+4[/tex]
[tex]$\Rightarrow\frac{1}{2} x+4=-\frac{1}{2} x+4[/tex]
Subtract 4 from both sides of the equation.
[tex]$\Rightarrow\frac{1}{2} x+4-4=-\frac{1}{2} x+4-4[/tex]
[tex]$\Rightarrow\frac{1}{2} x=-\frac{1}{2} x[/tex]
Arrange like terms in one side of the equation.
Negative term changed to positive term when it goes to left side of the equation.
[tex]$\Rightarrow\frac{1}{2} x+\frac{1}{2} x=0[/tex]
[tex]$\Rightarrow\frac{1+1}{2} x=0[/tex]
[tex]$\Rightarrow\frac{2}{2} x=0[/tex]
[tex]$\Rightarrow x=0[/tex]
Option C is the correct answer.
The value of x is 0.
