Answer :
Sure! 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]
1. Distribute: First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side of the equation:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides: Combine like terms on both sides.
Left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
Right side:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides: This gives:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Solve for [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
Thus, 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]
1. Distribute: First, distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side of the equation:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides: Combine like terms on both sides.
Left side:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
Right side:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides: This gives:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Solve for [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Simplify:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
