Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
Given equation:
[tex]\[
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4)
\][/tex]
Step 1: Expand and simplify both sides of the equation.
Left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, the equation is:
[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]
[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]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
Given equation:
[tex]\[
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4)
\][/tex]
Step 1: Expand and simplify both sides of the equation.
Left side:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
Right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now, the equation is:
[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]
[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]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
