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Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex]:
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
- On the left-hand side, distribute [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right-hand side, distribute and simplify:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Step 2: Equate the simplified expressions from both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Move all [tex]\( x \)[/tex] terms to one side:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Step 5: Combine the [tex]\( x \)[/tex] terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation is:
[tex]\[
\boxed{0}
\][/tex]
The original equation is:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
- On the left-hand side, distribute [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \times x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right-hand side, distribute and simplify:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
Step 2: Equate the simplified expressions from both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Move all [tex]\( x \)[/tex] terms to one side:
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Step 5: Combine the [tex]\( x \)[/tex] terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation is:
[tex]\[
\boxed{0}
\][/tex]
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