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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 :

Let's solve the equation step-by-step together.

We need to solve this equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]

### Step 1: Distribute and Simplify
Start by simplifying both sides:

- On the left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplifying gives:
[tex]\[
\frac{1}{2}x + 4
\][/tex]

- On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplifying gives:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]

### Step 2: Set the Simplified Equation
Now the equation simplifies to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

### Step 3: Subtract 4 from Both Sides
Subtract 4 from each side:
[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 the [tex]\( x\)[/tex]-terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]

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

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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