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. 0
D. [tex]\(\frac{1}{2}\)[/tex]

Answer :

To solve the equation Karissa has been working on, we'll continue from where she left off to find the value of [tex]\( x \)[/tex].

Here's the equation Karissa reached:

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

First, let's subtract 4 from both sides to simplify the equation:

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

Next, to eliminate the negative term on the right, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Combine the terms on the left:

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

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

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