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

Answer :

Let's solve the equation 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]

Karissa's work simplifies it as follows:

1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:

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

2. Simplify inside the parentheses on the right side:

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

3. Combine like terms:

[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

Next, we need to isolate [tex]\( x \)[/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 to get all the [tex]\( x \)[/tex] terms on one side:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

Simplifying gives:

[tex]\[
x = 0
\][/tex]

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