Sure! Let's solve for [tex]\( w \)[/tex] in the equation [tex]\( y - a w = 2 w - 1 \)[/tex].
1. Write down the original equation:
[tex]\[
y - a w = 2 w - 1
\][/tex]
2. Isolate the terms involving [tex]\( w \)[/tex] on one side of the equation. To do this, we need to move all terms involving [tex]\( w \)[/tex] to one side and the constant terms to the other:
First, add [tex]\( a w \)[/tex] to both sides to get:
[tex]\[
y = 2 w - 1 + a w
\][/tex]
Next, combine like terms involving [tex]\( w \)[/tex]:
[tex]\[
y = w (2 + a) - 1
\][/tex]
3. Isolate the constant term on the other side:
Add 1 to both sides to move the constant term to the left side of the equation:
[tex]\[
y + 1 = w (2 + a)
\][/tex]
4. Solve for [tex]\( w \)[/tex]:
Finally, divide both sides by [tex]\( 2 + a \)[/tex] to isolate [tex]\( w \)[/tex]:
[tex]\[
w = \frac{y + 1}{2 + a}
\][/tex]
So, the solution is:
[tex]\[
w = \frac{y + 1}{2 + a}
\][/tex]
