Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex], let's work through the steps Karissa took:
1. Distribute and simplify both sides:
- The left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- The right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex]. Simplifying inside the parentheses first gives us [tex]\(\frac{1}{2}x - x + 4\)[/tex].
2. Combine the terms:
- The equation becomes [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex].
3. Subtract 4 from both sides:
- [tex]\(\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4\)[/tex] simplifies to [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
- [tex]\(\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x\)[/tex] simplifies to [tex]\(x = 0\)[/tex].
So, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
1. Distribute and simplify both sides:
- The left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- The right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex]. Simplifying inside the parentheses first gives us [tex]\(\frac{1}{2}x - x + 4\)[/tex].
2. Combine the terms:
- The equation becomes [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex].
3. Subtract 4 from both sides:
- [tex]\(\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4\)[/tex] simplifies to [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
- [tex]\(\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x\)[/tex] simplifies to [tex]\(x = 0\)[/tex].
So, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
