Answer :
Sure! Let's solve the equation step-by-step based on Karissa's work:
1. Original Equation:
[tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex]
2. Distribute and Simplify the Left Side:
[tex]\(\frac{1}{2} \times (x-14) = \frac{1}{2}x - 7\)[/tex]
So, the left side becomes:
[tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
3. Simplify the Right Side:
Distribute the negative sign:
[tex]\(\frac{1}{2}x - x + 4\)[/tex]
4. Equations After Distribution:
So, the equation now looks like this:
[tex]\(\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4\)[/tex]
5. Further Simplify Both Sides:
The left side stays: [tex]\(\frac{1}{2}x + 4\)[/tex]
The right side simplifies to: [tex]\(-\frac{1}{2}x + 4\)[/tex]
6. Equate and Solve for [tex]\(x\)[/tex]:
Set up the equation:
[tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex]
7. Subtract 4 from Both Sides:
[tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex]
8. Combine Like Terms:
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]
[tex]\(x = 0\)[/tex]
The value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Original Equation:
[tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex]
2. Distribute and Simplify the Left Side:
[tex]\(\frac{1}{2} \times (x-14) = \frac{1}{2}x - 7\)[/tex]
So, the left side becomes:
[tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
3. Simplify the Right Side:
Distribute the negative sign:
[tex]\(\frac{1}{2}x - x + 4\)[/tex]
4. Equations After Distribution:
So, the equation now looks like this:
[tex]\(\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4\)[/tex]
5. Further Simplify Both Sides:
The left side stays: [tex]\(\frac{1}{2}x + 4\)[/tex]
The right side simplifies to: [tex]\(-\frac{1}{2}x + 4\)[/tex]
6. Equate and Solve for [tex]\(x\)[/tex]:
Set up the equation:
[tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex]
7. Subtract 4 from Both Sides:
[tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex]
8. Combine Like Terms:
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]
[tex]\(x = 0\)[/tex]
The value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].