Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4)\)[/tex], Karissa's work progresses as follows:
1. Start by simplifying both sides of the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
3. Simplify further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
4. On the right side, distribute the minus sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
5. Combine the terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
6. Equate both simplified expressions:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
7. Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
8. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
9. Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the solution to the equation is [tex]\(x = 0\)[/tex].
1. Start by simplifying both sides of the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
3. Simplify further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
4. On the right side, distribute the minus sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
5. Combine the terms:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
6. Equate both simplified expressions:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
7. Subtract 4 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
8. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
9. Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the solution to the equation is [tex]\(x = 0\)[/tex].
