Answer :
Let's solve the equation step by step just like Karissa did:
1. The equation begins as:
[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]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
- On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine like terms [tex]\(\frac{1}{2}x - x\)[/tex]:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
4. This gives us the simplified equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract [tex]\(4\)[/tex] from both sides to isolate the terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all [tex]\(x\)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
7. Combine the terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(\boxed{0}\)[/tex].
1. The equation begins as:
[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]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
- On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine like terms [tex]\(\frac{1}{2}x - x\)[/tex]:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
4. This gives us the simplified equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract [tex]\(4\)[/tex] from both sides to isolate the terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all [tex]\(x\)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
7. Combine the terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(\boxed{0}\)[/tex].
