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Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
We start with the given equation:
[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:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/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 through [tex]\( (x-4) \)[/tex]:
[tex]\[
-x + 4
\][/tex]
So, the right side becomes:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Thus, the equation simplifies to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides.
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[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]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
We start with the given equation:
[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:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/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 through [tex]\( (x-4) \)[/tex]:
[tex]\[
-x + 4
\][/tex]
So, the right side becomes:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Thus, the equation simplifies to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides.
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[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]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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