College

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.

\[
\begin{align*}
\frac{1}{2}(x-14)+11 & = \frac{1}{2} x-(x-4) \\
\frac{1}{2} x-7+11 & = \frac{1}{2} x-x+4 \\
\frac{1}{2} x+4 & = -\frac{1}{2} x+4 \\
\end{align*}
\]

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. 0
C. [tex]-\frac{1}{2}[/tex]
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 after Karissa's simplifications:
[tex]\[ \frac{1}{2}x + 4 = -\frac{1}{2}x + 4 \][/tex]

1. Subtract 4 from both sides to eliminate the constants:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

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

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

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