To solve the equation [tex]\( M = 2P + 3Q \)[/tex] for the variable [tex]\( P \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
M = 2P + 3Q
\][/tex]
2. Isolate the term containing [tex]\( P \)[/tex] on one side of the equation. To do this, subtract [tex]\( 3Q \)[/tex] from both sides:
[tex]\[
M - 3Q = 2P
\][/tex]
3. Solve for [tex]\( P \)[/tex] by dividing both sides of the equation by 2:
[tex]\[
P = \frac{M - 3Q}{2}
\][/tex]
Thus, the solution for [tex]\( P \)[/tex] in terms of [tex]\( M \)[/tex] and [tex]\( Q \)[/tex] is:
[tex]\[
P = \frac{M - 3Q}{2}
\][/tex]
Comparing this with the choices provided:
1. [tex]\(\boxed{P = \frac{M - 3Q}{2}}\)[/tex]
2. [tex]\(Q = \frac{M - 2P}{3}\)[/tex]
3. [tex]\(P = \frac{M + 3Q}{2}\)[/tex]
4. [tex]\(P = 2(M - 3Q)\)[/tex]
The correct choice is the first one:
[tex]\[
P = \frac{M - 3Q}{2}
\][/tex]
