Answer :
Let's go through the solution to find the value of [tex]\( x \)[/tex] step-by-step:
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Simplify both sides:
- Distribute [tex]\( \frac{1}{2} \)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- Simplify the left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So, the equation now looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to simplify:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine the terms on the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
1. Start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Simplify both sides:
- Distribute [tex]\( \frac{1}{2} \)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
This becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- Simplify the left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- Distribute the negative sign on the right side:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
- Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So, the equation now looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to simplify:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine the terms on the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
