Answer :
Let's solve the equation step-by-step.
We start with the equation provided in Karissa's work:
1. [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex]
First, let's apply the distributive property on both sides to simplify:
2. [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4\)[/tex]
Now, combine like terms:
3. [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex]
Next, subtract 4 from both sides of the equation:
4. [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex]
To solve for [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all the terms involving [tex]\(x\)[/tex] on one side:
5. [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex]
Simplify the left side:
6. [tex]\(x = 0\)[/tex]
Thus, the value of [tex]\(x\)[/tex] is 0.
We start with the equation provided in Karissa's work:
1. [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)\)[/tex]
First, let's apply the distributive property on both sides to simplify:
2. [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4\)[/tex]
Now, combine like terms:
3. [tex]\(\frac{1}{2}x + 4 = -\frac{1}{2}x + 4\)[/tex]
Next, subtract 4 from both sides of the equation:
4. [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex]
To solve for [tex]\(x\)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all the terms involving [tex]\(x\)[/tex] on one side:
5. [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex]
Simplify the left side:
6. [tex]\(x = 0\)[/tex]
Thus, the value of [tex]\(x\)[/tex] is 0.
