Answer :
Let's find the value of [tex]\( x \)[/tex] in the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Karissa has already made some progress in simplifying the equation. Let's follow through her steps:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
2. Simplify the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
This becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
3. Set the simplified forms from both sides of the equation equal to each other:
[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 simplify:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
6. Combine the terms:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Karissa has already made some progress in simplifying the equation. Let's follow through her steps:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
2. Simplify the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
This becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
3. Set the simplified forms from both sides of the equation equal to each other:
[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 simplify:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
6. Combine the terms:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
