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Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
Karissa's equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, we simplify each side of the equation:
- On the left side:
- Distribute [tex]\(\frac{1}{2}\)[/tex] across [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- Add 11:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- On the right side:
- Distribute the subtraction over [tex]\((x-4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4 = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, the simplified equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
Karissa's equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, we simplify each side of the equation:
- On the left side:
- Distribute [tex]\(\frac{1}{2}\)[/tex] across [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- Add 11:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- On the right side:
- Distribute the subtraction over [tex]\((x-4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4 = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, the simplified equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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