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Answer :
Sure! Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
We start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] into the terms inside the parentheses on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
So, the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Combine like terms on the left side:
[tex]\[
-7 + 11 = 4
\][/tex]
So, the equation is now:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x-4)
\][/tex]
3. Simplify the right side by distributing the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
We start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] into the terms inside the parentheses on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
So, the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
2. Combine like terms on the left side:
[tex]\[
-7 + 11 = 4
\][/tex]
So, the equation is now:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - (x-4)
\][/tex]
3. Simplify the right side by distributing the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
This simplifies to:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
4. Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
5. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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