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Alimmhmins solves the equation:

[tex]\[

\left(x = -1 + y + y = \frac{1}{2} x - (x-4)\right.

\][/tex]

Her work is correct and is shown below:

[tex]\[

\begin{aligned}

\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{aligned}

\][/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 :

To solve the equation [tex]\(\frac{1}{2} x = -\frac{1}{2} x\)[/tex], let's carefully go through the steps:

1. Initial Setup: We start with the equation [tex]\(\frac{1}{2} x = -\frac{1}{2} x\)[/tex].

2. Isolate the Variable: Add [tex]\(\frac{1}{2} x\)[/tex] to both sides of the equation to get all terms involving [tex]\(x\)[/tex] on one side:

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

3. Simplify:

[tex]\[
1x = 0
\][/tex]

4. Calculate the Value of [tex]\(x\)[/tex]: This simplifies to [tex]\(x = 0\)[/tex].

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

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