Answer :
Sure! Let's solve the equation step-by-step.
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
1. Distribute on the left side:
- Start with [tex]\(\frac{1}{2}(x-14)\)[/tex]. When you distribute [tex]\(\frac{1}{2}\)[/tex], you get:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- Add 11 to [tex]\(\frac{1}{2}x - 7\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
2. Simplify the right side:
- The right side [tex]\(\frac{1}{2}x - (x-4)\)[/tex] becomes:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Combine the terms:
[tex]\[
(-\frac{1}{2}x) + 4
\][/tex]
3. At this point, the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
1. Distribute on the left side:
- Start with [tex]\(\frac{1}{2}(x-14)\)[/tex]. When you distribute [tex]\(\frac{1}{2}\)[/tex], you get:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
- Add 11 to [tex]\(\frac{1}{2}x - 7\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
2. Simplify the right side:
- The right side [tex]\(\frac{1}{2}x - (x-4)\)[/tex] becomes:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Combine the terms:
[tex]\[
(-\frac{1}{2}x) + 4
\][/tex]
3. At this point, the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
