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Answer :
Let's solve the equation step by step and find the value of [tex]\( x \)[/tex].
The equation Karissa starts with is:
[tex]\[
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)
\][/tex]
Step 1: Simplify both sides
First, let's distribute and combine like terms on both sides of the equation:
- Left side: [tex]\(\frac{1}{2}(x-14) + 11\)[/tex]
- Distribute [tex]\(\frac{1}{2}\)[/tex]: [tex]\(\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7\)[/tex]
- Combine: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]
- Distribute the negative sign: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
- Simplify: [tex]\(\left(\frac{1}{2} - 1\right)x + 4 = -\frac{1}{2}x + 4\)[/tex]
Now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Set the equation
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the term on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
The equation Karissa starts with is:
[tex]\[
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)
\][/tex]
Step 1: Simplify both sides
First, let's distribute and combine like terms on both sides of the equation:
- Left side: [tex]\(\frac{1}{2}(x-14) + 11\)[/tex]
- Distribute [tex]\(\frac{1}{2}\)[/tex]: [tex]\(\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7\)[/tex]
- Combine: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
- Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]
- Distribute the negative sign: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
- Simplify: [tex]\(\left(\frac{1}{2} - 1\right)x + 4 = -\frac{1}{2}x + 4\)[/tex]
Now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Set the equation
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the term on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{0}\)[/tex].
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