Karissa begins to solve the equation [tex]\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)[/tex]. Her work is correct and is shown below:

[tex]
\begin{array}{c}
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4) \\
\frac{1}{2} x-7+11=\frac{1}{2} x-x+4 \\
\frac{1}{2} x+4=-\frac{1}{2} x+4 \\
\end{array}
[/tex]

When she subtracts 4 from both sides, [tex]\frac{1}{2} x=-\frac{1}{2} x[/tex] results. What is the value of [tex]x[/tex]?

A. -1
B. [tex]p[/tex]
C. [tex]\frac{1}{2}[/tex]
D. 0
E. [tex]\frac{1}{2}[/tex]

Answer :

Sure! Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].

We start with the equation:

[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

Step 1: Distribute and simplify both sides of the equation:

- On the left side:
[tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].

- On the right side:
[tex]\(\frac{1}{2}x - (x-4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex], which simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].

So the equation now is:

[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Step 2: Subtract 4 from both sides to isolate the terms involving [tex]\( x \)[/tex]:

[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Step 3: 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]

[tex]\[
x = 0
\][/tex]

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].