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Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
The equation given is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute terms and simplify both sides
On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] across [tex]\( (x-14) \)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
So the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Simplifying the right side, it becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
The equation is now:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Cancel out common terms
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: 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]
Thus, the value of [tex]\( x \)[/tex] is 0.
The equation given is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute terms and simplify both sides
On the left side, distribute [tex]\(\frac{1}{2}\)[/tex] across [tex]\( (x-14) \)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
So the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Simplifying the right side, it becomes:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
The equation is now:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Cancel out common terms
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: 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]
Thus, the value of [tex]\( x \)[/tex] is 0.
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