Answer :
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] to [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- On the right side, distribute the negative sign inside the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
So we have:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Combine like terms
- On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine [tex]\(\frac{1}{2}x\)[/tex] and [tex]\(-x\)[/tex], which gives:
[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 3: Subtract 4 from both sides
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, 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] to [tex]\((x-14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
- On the right side, distribute the negative sign inside the parentheses:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
So we have:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Combine like terms
- On the left side, combine [tex]\(-7\)[/tex] and [tex]\(11\)[/tex]:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, combine [tex]\(\frac{1}{2}x\)[/tex] and [tex]\(-x\)[/tex], which gives:
[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 3: Subtract 4 from both sides
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].