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Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex]:
1. Start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute the [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]
Simplifying, we get:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
On the left side:
[tex]\[
-7 + 11 = 4
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - x = -\frac{1}{2}x
\][/tex]
Therefore, the right side becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
4. Now, the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Combine all [tex]\( x \)[/tex] terms on one side by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying, we get:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
1. Start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Distribute the [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]
Simplifying, we get:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
3. Simplify both sides:
On the left side:
[tex]\[
-7 + 11 = 4
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - x = -\frac{1}{2}x
\][/tex]
Therefore, the right side becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
4. Now, the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
5. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
6. Combine all [tex]\( x \)[/tex] terms on one side by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying, we get:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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