College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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 carefully go through the steps:

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

2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on both sides:
- Left side: [tex]\(\frac{1}{2}(x) - \frac{1}{2}(14) + 11 = \frac{1}{2}x - 7 + 11\)[/tex]
- Right side: [tex]\(\frac{1}{2}x - x + 4\)[/tex]

3. Simplify both sides:
- Left side becomes: [tex]\(\frac{1}{2}x + 4\)[/tex]
- Right side becomes: [tex]\(-\frac{1}{2}x + 4\)[/tex]

4. Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

5. Subtract 4 from both sides to eliminate the constants:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

6. 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]
[tex]\[
x = 0
\][/tex]

Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].