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 :

To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's follow the steps shown in Karissa's work.

1. Distribute and simplify both sides:

Start with the original equation:

[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

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

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

Distribute the negative sign on the right side:

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

Simplify both sides:

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

2. Eliminate constants from both sides:

Subtract 4 from both sides of the equation:

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

3. Solve for [tex]\(x\)[/tex]:

Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate [tex]\(x\)[/tex]:

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

Simplify:

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

The value of [tex]\(x\)[/tex] is 0. This is the solution to the equation.