High School

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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 :

Let's solve the equation step-by-step to find the value of [tex]\(x\)[/tex].

The original equation provided is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

First, simplify both sides of the equation.

Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]

This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

On the right side, distribute the subtraction:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]

Which simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

So, we have the equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Next, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Simplify the left side:
[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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