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:

[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 :

To solve the equation Karissa was working on, let's go through the steps:

We start from the equation at the point where Karissa left off:

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

Subtract 4 from both sides to isolate the terms with [tex]\( x \)[/tex]:

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

To eliminate the fractions and solve for [tex]\( x \)[/tex], let's combine like terms. We'll add [tex]\(\frac{1}{2}x\)[/tex] to both sides to simplify:

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

This simplifies to:

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

Thus, the value of [tex]\( x \)[/tex] that satisfies the equation is [tex]\( \boxed{0} \)[/tex].