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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 :

Sure, let's solve the equation step by step.

We start with the given equation:

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

Step 1: Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:

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

This simplifies to:

[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

Step 2: Simplify both sides:

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

Step 3: Combine like terms on the right side:

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

Step 4: Subtract 4 from both sides:

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

Step 5: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:

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

Step 6: Simplify:

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

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

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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