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Answer :
To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)\)[/tex], let’s follow these steps:
1. Distribute and Simplify:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
Distribute the [tex]\(\frac{1}{2}\)[/tex] in the first term:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]
2. Combine Like Terms:
Simplify both sides of the equation:
[tex]\[
\frac{1}{2} x + 4 = \frac{1}{2} x - x + 4
\][/tex]
3. Eliminate Terms:
To solve this equation, subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]
4. Isolate x:
Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to help isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]
5. Solve for x:
Combine the x terms on the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
1. Distribute and Simplify:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4)
\][/tex]
Distribute the [tex]\(\frac{1}{2}\)[/tex] in the first term:
[tex]\[
\frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4
\][/tex]
2. Combine Like Terms:
Simplify both sides of the equation:
[tex]\[
\frac{1}{2} x + 4 = \frac{1}{2} x - x + 4
\][/tex]
3. Eliminate Terms:
To solve this equation, subtract 4 from both sides:
[tex]\[
\frac{1}{2} x = -\frac{1}{2} x
\][/tex]
4. Isolate x:
Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to help isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{2} x + \frac{1}{2} x = 0
\][/tex]
5. Solve for x:
Combine the x terms on the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is [tex]\(0\)[/tex].
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