Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)\)[/tex], let's follow these steps:
1. Distribute the terms:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] through [tex]\((x - 14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- On the right side, first simplify inside the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
- Combine the constants on the left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- The right side becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
3. Set the simplified expressions equal to each other:
[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. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute the terms:
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] through [tex]\((x - 14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- On the right side, first simplify inside the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
- Combine the constants on the left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- The right side becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
3. Set the simplified expressions equal to each other:
[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. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
- Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
