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Answer :
Sure! Let's solve the equation step-by-step and find the value of [tex]\( x \)[/tex].
The equation given is:
[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]\[
\frac{1}{2} x - \frac{1}{2} \times 14 + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]
Step 2: Simplify both sides of the equation:
On the left side:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2} x - x + 4 = -\frac{1}{2} x + 4
\][/tex]
So now the equation is:
[tex]\[
\frac{1}{2} x + 4 = -\frac{1}{2} x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to get:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]
Step 5: Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 0.
The equation given is:
[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]\[
\frac{1}{2} x - \frac{1}{2} \times 14 + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]
Step 2: Simplify both sides of the equation:
On the left side:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2} x - x + 4 = -\frac{1}{2} x + 4
\][/tex]
So now the equation is:
[tex]\[
\frac{1}{2} x + 4 = -\frac{1}{2} x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to get:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]
Step 5: Combine like terms:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 0.
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