High School

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, [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:

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

1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11
\][/tex]
Simplifying this gives:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

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

3. Simplify the right side:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

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

5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

6. Combine the terms:
[tex]\[
x = 0
\][/tex]

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