Answer :
Certainly! Let's go through the steps to solve the equation carefully:
We start with the equation Karissa worked on:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
1. Distribute and simplify each side:
The left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
After simplifying, it becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
The right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplifying it, you get:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
2. Write the simplified equation:
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
When you subtract 4 from each side, the equation becomes:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine like terms:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying the left side gives:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is 0. This means that when you solve the equation using these steps, you find that [tex]\(x = 0\)[/tex] satisfies the equation.
We start with the equation Karissa worked on:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
1. Distribute and simplify each side:
The left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
After simplifying, it becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
The right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplifying it, you get:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
2. Write the simplified equation:
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
When you subtract 4 from each side, the equation becomes:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine like terms:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying the left side gives:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is 0. This means that when you solve the equation using these steps, you find that [tex]\(x = 0\)[/tex] satisfies the equation.
