Answer :
Certainly! Let's solve the equation step-by-step:
The original equation is:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Distribute and simplify both sides.
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify the numbers:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Step 2: Set the simplified expressions from each side equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Solve for [tex]\(x\)[/tex].
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The original equation is:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Distribute and simplify both sides.
- On the left side, distribute [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify the numbers:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Combine like terms [tex]\(\frac{1}{2}x - x = -\frac{1}{2}x\)[/tex]:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Step 2: Set the simplified expressions from each side equal:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract [tex]\(4\)[/tex] from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Solve for [tex]\(x\)[/tex].
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
