Answer :
Sure! Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
The given equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, we need to simplify both sides of the equation.
### Step 1: Distribute and simplify
Starting with the left-hand side (LHS):
[tex]\[
\frac{1}{2}(x-14) + 11
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] inside the parenthesis:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify further:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Now, for the right-hand side (RHS):
[tex]\[
\frac{1}{2}x - (x - 4)
\][/tex]
Distribute the negative sign inside the parenthesis:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, our equation looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
### Step 2: Subtract 4 from both sides
Subtracting 4 from both sides of the equation:
[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: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides
Adding [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation:
[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]\[
\boxed{0}
\][/tex]
The given equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, we need to simplify both sides of the equation.
### Step 1: Distribute and simplify
Starting with the left-hand side (LHS):
[tex]\[
\frac{1}{2}(x-14) + 11
\][/tex]
Distribute [tex]\(\frac{1}{2}\)[/tex] inside the parenthesis:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify further:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Now, for the right-hand side (RHS):
[tex]\[
\frac{1}{2}x - (x - 4)
\][/tex]
Distribute the negative sign inside the parenthesis:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, our equation looks like this:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
### Step 2: Subtract 4 from both sides
Subtracting 4 from both sides of the equation:
[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: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides
Adding [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation:
[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]\[
\boxed{0}
\][/tex]
