Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Karissa's work simplifies it as follows:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Simplify inside the parentheses on the right side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, we need to isolate [tex]\( x \)[/tex].
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all the [tex]\( x \)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying gives:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Karissa's work simplifies it as follows:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Simplify inside the parentheses on the right side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, we need to isolate [tex]\( x \)[/tex].
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all the [tex]\( x \)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying gives:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
