College

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. [tex]\(-1\)[/tex]

B. [tex]\(\frac{1}{2}\)[/tex]

C. [tex]\(0\)[/tex]

D. [tex]\(\frac{1}{2}\)[/tex]

Answer :

Let's solve the equation step-by-step:

1. Karissa has simplified the original equation to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

2. The next step is to subtract 4 from both sides to make it simpler:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

3. To solve for [tex]\( x \)[/tex], you can add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate [tex]\(-\frac{1}{2}x\)[/tex] from one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

4. Simplifying the left side, you get:
[tex]\[
x = 0
\][/tex]

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