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 :

Sure, let's solve the equation step by step:

1. Start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]

2. Distribute and simplify both sides:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]

3. Further simplify by combining like terms:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/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 x terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

6. Combine the x terms:
[tex]\[
x = 0
\][/tex]

The value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].