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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: 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]
Thus, the equation simplifies to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides.
This gives:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to solve for [tex]\( x \)[/tex].
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[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: 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]
Thus, the equation simplifies to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides.
This gives:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to solve for [tex]\( x \)[/tex].
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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