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 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. -1
B. [tex]\frac{1}{2}[/tex]
C. 0
D. [tex]\frac{1}{2}[/tex]

Answer :

Alright, let's solve the equation step-by-step clearly.

Starting with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

1. Distribute [tex]\(\frac{1}{2}\)[/tex] on both sides:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

2. Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

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

5. Simplify the equation:
[tex]\[
x = 0
\][/tex]

So, the solution to the equation is:
[tex]\[
x = 0
\][/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 shown below. 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!

Rewritten by : Barada