To solve for [tex]\( x \)[/tex] in the equation
[tex]\[
\frac{2x - 3}{3x + 2} = wh
\][/tex]
we need to isolate [tex]\( x \)[/tex]. Here are the steps we should follow:
1. Eliminate the fraction: We can do this by multiplying both sides of the equation by [tex]\( 3x + 2 \)[/tex].
[tex]\[
2x - 3 = wh (3x + 2)
\][/tex]
2. Distribute [tex]\( wh \)[/tex] on the right side:
[tex]\[
2x - 3 = wh \cdot 3x + wh \cdot 2
\][/tex]
[tex]\[
2x - 3 = 3whx + 2wh
\][/tex]
3. Collect all [tex]\( x \)[/tex] terms on one side of the equation and constant terms on the other side:
[tex]\[
2x - 3whx = 2wh + 3
\][/tex]
4. Factor out [tex]\( x \)[/tex] from the left side:
[tex]\[
x(2 - 3wh) = 2wh + 3
\][/tex]
5. Solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\( 2 - 3wh \)[/tex] (assuming [tex]\( 2 - 3wh \neq 0 \)[/tex]):
[tex]\[
x = \frac{2wh + 3}{2 - 3wh}
\][/tex]
So the value of [tex]\( x \)[/tex] is:
[tex]\[
x = \frac{2wh + 3}{2 - 3wh}
\][/tex]
