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Answer :
Sure! Let's solve the equation step-by-step:
The given equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, we distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \cdot 14 = \frac{1}{2}x - 7
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Next, we simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Now, we simplify the right side. Distribute the negative sign inside the parentheses:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Now our equation looks like:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Let's combine like terms on the right side. We know [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This reduces to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To clear the fraction, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The given equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, we distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \cdot 14 = \frac{1}{2}x - 7
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Next, we simplify the left side by combining like terms:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Now, we simplify the right side. Distribute the negative sign inside the parentheses:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Now our equation looks like:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Let's combine like terms on the right side. We know [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, subtract 4 from both sides to simplify:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This reduces to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To clear the fraction, add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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