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Answer :
Sure! Let's solve the equation step by step to find the value of [tex]\( x \)[/tex]:
The initial equation is:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, distribute and simplify both sides:
1. Expand [tex]\(\frac{1}{2}(x - 14)\)[/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]
2. Now, simplify the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now we have the equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate the terms with [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying this, we get:
[tex]\[
x = 0
\][/tex]
Thus, the solution is [tex]\( x = 0 \)[/tex].
The initial equation is:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
First, distribute and simplify both sides:
1. Expand [tex]\(\frac{1}{2}(x - 14)\)[/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]
2. Now, simplify the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now we have the equation:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Subtract 4 from both sides to isolate the terms with [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplifying this, we get:
[tex]\[
x = 0
\][/tex]
Thus, the solution is [tex]\( x = 0 \)[/tex].
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