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. [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 to find the value of [tex]\( x \)[/tex].

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

Step 1: Simplify each side of the equation

Start by expanding and simplifying each expression:
- For the left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

- For the right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify further:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

Now our equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Step 2: Eliminate constants

Subtract 4 from both sides to eliminate the constant:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Step 3: Solve for [tex]\( x \)[/tex]

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

So, 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 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