Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let's go through the process step by step:
1. Distribute and simplify each side of the equation:
- On the left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplifying further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplifying further:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
2. Match the simplified equations on both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides to eliminate the constant:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. 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]
5. This simplifies to:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Distribute and simplify each side of the equation:
- On the left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplifying further:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplifying further:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
2. Match the simplified equations on both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides to eliminate the constant:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. 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]
5. This simplifies to:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
