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Answer :
Sure, let's work through the solution step-by-step to find the value of [tex]\(x\)[/tex] for the given equation:
1. Start with the equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute and simplify both sides:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
On the left side: [tex]\(\frac{1}{2}x - 7 + 11\)[/tex] simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
On the right side, simplify: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex].
Now, the equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine like terms:
To get rid of the fractions, you can add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
1. Start with the equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
2. Distribute and simplify both sides:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
On the left side: [tex]\(\frac{1}{2}x - 7 + 11\)[/tex] simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
On the right side, simplify: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex].
Now, the equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Combine like terms:
To get rid of the fractions, you can add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
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