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, the equation

[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 :

Certainly! Let's solve the equation step-by-step:

The original equation is:

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

Step 1: Distribute and simplify both sides.

- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex]:

[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]

Simplify the numbers:

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

- On the right side, distribute the negative sign:

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

Combine like terms [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]:

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

Step 2: Set the simplified expressions from each side equal:

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

Step 3: Subtract [tex]\(4\)[/tex] from both sides:

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

Step 4: Solve for [tex]\(x\)[/tex].

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

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

This simplifies to:

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

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