Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through it step by step:
1. Simplify both sides of the equation:
Start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine like terms:
On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Eliminate terms:
Now, subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
4. Combine terms on the right side:
On the right side, combine [tex]\(\frac{1}{2}x - x\)[/tex]:
[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]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Simplify both sides of the equation:
Start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Combine like terms:
On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
3. Eliminate terms:
Now, subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
4. Combine terms on the right side:
On the right side, combine [tex]\(\frac{1}{2}x - x\)[/tex]:
[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]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
