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. 0
D. [tex]\(\frac{1}{2}\)[/tex]

Answer :

Sure, let's walk through the problem step by step to find the value of [tex]\( x \)[/tex].

We start with the 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]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]

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

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

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

Step 4: Simplify the right side by combining terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

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

This simplifies to:
[tex]\[
x = 0
\][/tex]

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