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Answer :
Let's solve the equation step by step.
We start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Simplify both sides
First, we'll expand each side.
- On the left side:
[tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] simplifies to [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which further simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side:
[tex]\(\frac{1}{2}x - (x - 4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex], which simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].
So now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Eliminate constant terms
To remove the constant terms, we subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Now, we add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate the variable:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This becomes:
[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]
Step 1: Simplify both sides
First, we'll expand each side.
- On the left side:
[tex]\(\frac{1}{2}(x - 14) + 11\)[/tex] simplifies to [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which further simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side:
[tex]\(\frac{1}{2}x - (x - 4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex], which simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].
So now the equation looks like:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Eliminate constant terms
To remove the constant terms, we subtract 4 from both sides:
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Now, we add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate the variable:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This becomes:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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