Answer :
Sure! Let's solve the equation 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 and simplify both sides of the equation:
- On the left side:
[tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side:
[tex]\(\frac{1}{2}x - (x-4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex], which simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].
So the equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: 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]
[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 and simplify both sides of the equation:
- On the left side:
[tex]\(\frac{1}{2}(x-14) + 11\)[/tex] becomes [tex]\(\frac{1}{2}x - 7 + 11\)[/tex], which simplifies to [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side:
[tex]\(\frac{1}{2}x - (x-4)\)[/tex] becomes [tex]\(\frac{1}{2}x - x + 4\)[/tex], which simplifies to [tex]\(-\frac{1}{2}x + 4\)[/tex].
So the equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: 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]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
