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Answer :
Let's solve the equation step-by-step:
Karissa started with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, she expanded both sides:
- On the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
- On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
The equation becomes:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Next, she simplifies both sides:
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Combine like terms on the right side:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Bring all the x terms to one side by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
Karissa started with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, she expanded both sides:
- On the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
- On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
The equation becomes:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Next, she simplifies both sides:
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Combine like terms on the right side:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Bring all the x terms to one side by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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