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Answer :
Sure! Let's solve the equation step by step:
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides
First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Next, combine the constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Simplify the right side by handling the terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Get [tex]\(x\)[/tex] terms on one side
Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Let's analyze [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex]. By adding [tex]\(\frac{1}{2}x\)[/tex] to both sides, you get:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation is [tex]\(x = 0\)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides
First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Next, combine the constants on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Simplify the right side by handling the terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Get [tex]\(x\)[/tex] terms on one side
Subtract 4 from both sides to eliminate the constant term:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Let's analyze [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex]. By adding [tex]\(\frac{1}{2}x\)[/tex] to both sides, you get:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation is [tex]\(x = 0\)[/tex].
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