Answer :
To solve the given equation [tex]\(\frac{1}{2}(x-14)+11 = \frac{1}{2}x - (x-4)\)[/tex], let's go through the steps Karissa followed:
1. Distribute and Simplify:
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Start by distributing the [tex]\(\frac{1}{2}\)[/tex] on the left-hand side:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine Like Terms:
Combine like terms on both sides:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Isolate the Variable:
Subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine and Solve:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] from the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
So, Karissa's solution indicates that the value of [tex]\(x\)[/tex] is indeed [tex]\(0\)[/tex].
1. Distribute and Simplify:
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Start by distributing the [tex]\(\frac{1}{2}\)[/tex] on the left-hand side:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine Like Terms:
Combine like terms on both sides:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Isolate the Variable:
Subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine and Solve:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] from the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
So, Karissa's solution indicates that the value of [tex]\(x\)[/tex] is indeed [tex]\(0\)[/tex].
