Answer :
Sure, let's walk through the problem step by step to find the value of [tex]\( x \)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Step 4: Simplify the right side by combining terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 5: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine [tex]\( x \)[/tex]:
[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].
We start with the equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Combine like terms:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Step 4: Simplify the right side by combining terms:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 5: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine [tex]\( x \)[/tex]:
[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].
