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Answer :
Let's solve the equation step by step:
The given 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]
The left side simplifies to:
[tex]\[ \frac{1}{2}x + 4 \][/tex]
On the right side, distribute the negative sign:
[tex]\[ \frac{1}{2}x - x + 4 \][/tex]
Step 2: Setting the simplified equations equal to each other, we have:
[tex]\[ \frac{1}{2}x + 4 = \frac{1}{2}x - x + 4 \][/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 to isolate the variable [tex]\(x\)[/tex]:
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = 0 \][/tex]
Combine the terms:
[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]
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]
The left side simplifies to:
[tex]\[ \frac{1}{2}x + 4 \][/tex]
On the right side, distribute the negative sign:
[tex]\[ \frac{1}{2}x - x + 4 \][/tex]
Step 2: Setting the simplified equations equal to each other, we have:
[tex]\[ \frac{1}{2}x + 4 = \frac{1}{2}x - x + 4 \][/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 to isolate the variable [tex]\(x\)[/tex]:
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = 0 \][/tex]
Combine the terms:
[tex]\[ x = 0 \][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
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