Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's follow the steps shown in Karissa's work.
1. Distribute and simplify both sides:
Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Eliminate constants from both sides:
Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
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]
Simplify:
[tex]\[
x = 0
\][/tex]
The value of [tex]\(x\)[/tex] is 0. This is the solution to the equation.
1. Distribute and simplify both sides:
Start with the original equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Eliminate constants from both sides:
Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
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]
Simplify:
[tex]\[
x = 0
\][/tex]
The value of [tex]\(x\)[/tex] is 0. This is the solution to the equation.
