Sure, let's solve the equation [tex]\( w = 3b - 2a + 2 \)[/tex] for [tex]\( a \)[/tex]:
1. Start with the given equation:
[tex]\[
w = 3b - 2a + 2
\][/tex]
2. Isolate the term involving [tex]\( a \)[/tex]:
[tex]\[
w - 3b = -2a + 2
\][/tex]
3. Rearrange the equation to collect constants on one side:
[tex]\[
w - 3b - 2 = -2a
\][/tex]
4. Divide both sides by [tex]\(-2\)[/tex] to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{w - 3b - 2}{-2}
\][/tex]
5. Simplify the expression:
[tex]\[
a = \frac{-(w - 3b - 2)}{2}
\][/tex]
[tex]\[
a = \frac{-w + 3b + 2}{2}
\][/tex]
6. Rewrite in a more conventional form:
[tex]\[
a = \frac{3b}{2} - \frac{w}{2} + 1
\][/tex]
So, the solution for [tex]\( a \)[/tex] in terms of [tex]\( w \)[/tex] and [tex]\( b \)[/tex] is:
[tex]\[
a = \frac{3b}{2} - \frac{w}{2} + 1
\][/tex]
This expression represents [tex]\( a \)[/tex] fully isolated.
