Answer :
Let's solve the equation step by step to find the value of [tex]\(x\)[/tex]:
1. Write down the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute and simplify both sides:
- The left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- The right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Set the simplified left side equal to the simplified right side:
[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 solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
1. Write down the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute and simplify both sides:
- The left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
- The right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Set the simplified left side equal to the simplified right side:
[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 solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
