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Answer :
To solve the equation [tex]\( \frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4) \)[/tex], let's follow the steps that Karissa took:
1. Simplify both sides of the equation:
- On the left:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- On the right:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
This simplifies our equation to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Subtract 4 from both sides to isolate terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Combine the [tex]\( x \)[/tex]-terms:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides in order to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
1. Simplify both sides of the equation:
- On the left:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- On the right:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
This simplifies our equation to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
2. Subtract 4 from both sides to isolate terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
3. Combine the [tex]\( x \)[/tex]-terms:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides in order to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
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Rewritten by : Barada
