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Answer :
Certainly! Let's solve the given equation step-by-step:
The equation is:
[tex]\[
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)
\][/tex]
1. Distribute on the left side:
- Distribute [tex]\(\frac{1}{2}\)[/tex] to both terms inside the parentheses:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
- This simplifies to:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
- On the left side, combine [tex]\(-7 + 11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine terms:
- [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]
- So, the right side becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
- The equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
- This helps to isolate the terms containing [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Solve for [tex]\(x\)[/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]
- This becomes:
[tex]\[
x = 0
\][/tex]
So, the solution for [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The equation is:
[tex]\[
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)
\][/tex]
1. Distribute on the left side:
- Distribute [tex]\(\frac{1}{2}\)[/tex] to both terms inside the parentheses:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
- This simplifies to:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
- On the left side, combine [tex]\(-7 + 11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine terms:
- [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]
- So, the right side becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
- The equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
- This helps to isolate the terms containing [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Solve for [tex]\(x\)[/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]
- This becomes:
[tex]\[
x = 0
\][/tex]
So, the solution for [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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