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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 go through the steps Karissa took:
1. Distribute and Simplify:
- Start with [tex]\(\frac{1}{2}(x-14)+11\)[/tex] on the left side. Distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- So the expression becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- Combine the constants [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
2. Simplify the Right Side:
- The expression is [tex]\(\frac{1}{2}x - (x-4)\)[/tex]. Distribute the negative sign through the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Combine [tex]\(\frac{1}{2}x - x\)[/tex] to simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
3. Equate and Solve:
- Now, set the two sides equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from Both Sides:
- This results in:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- Simplify the left side:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute and Simplify:
- Start with [tex]\(\frac{1}{2}(x-14)+11\)[/tex] on the left side. Distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- So the expression becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- Combine the constants [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
2. Simplify the Right Side:
- The expression is [tex]\(\frac{1}{2}x - (x-4)\)[/tex]. Distribute the negative sign through the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Combine [tex]\(\frac{1}{2}x - x\)[/tex] to simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
3. Equate and Solve:
- Now, set the two sides equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from Both Sides:
- This results in:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- Simplify the left side:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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