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, the equation

[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 :

To solve the given equation step-by-step, let's start from where Karissa left off:

The simplified equation is [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].

1. Collect the [tex]\(x\)[/tex] terms on one side:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

2. Simplify the equation:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
x = 0
\][/tex]

The value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex]. Therefore, the correct answer is [tex]\(0\)[/tex].

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