To solve the equation [tex]\( 2\alpha - 11 = 25 - \alpha \)[/tex] for [tex]\(\alpha\)[/tex], we follow a series of steps to isolate [tex]\(\alpha\)[/tex]. Here’s the detailed step-by-step solution:
1. Move all [tex]\(\alpha\)[/tex] terms to one side of the equation:
Start with the given equation:
[tex]\[
2\alpha - 11 = 25 - \alpha
\][/tex]
Add [tex]\(\alpha\)[/tex] to both sides of the equation to move [tex]\(\alpha\)[/tex] terms to one side:
[tex]\[
2\alpha + \alpha - 11 = 25
\][/tex]
2. Simplify the terms:
Combine the [tex]\(\alpha\)[/tex] terms on the left side:
[tex]\[
3\alpha - 11 = 25
\][/tex]
3. Isolate the [tex]\(\alpha\)[/tex] term:
Add 11 to both sides of the equation to move the constant term to the right side:
[tex]\[
3\alpha = 25 + 11
\][/tex]
Simplify the right side:
[tex]\[
3\alpha = 36
\][/tex]
4. Solve for [tex]\(\alpha\)[/tex]:
Divide both sides of the equation by 3 to isolate [tex]\(\alpha\)[/tex]:
[tex]\[
\alpha = \frac{36}{3}
\][/tex]
Simplify the division:
[tex]\[
\alpha = 12
\][/tex]
Therefore, the solution to the equation [tex]\( 2\alpha - 11 = 25 - \alpha \)[/tex] is:
[tex]\[
\alpha = 12
\][/tex]
