Question

For which values of P and Q does the following equation have infinitely many solutions ?
-90x+Q=Px+45
Choose all answers that apply:

A
Q=45Q and P=-45

B
Q=-45Q and P=45P

C
Q=-45Q and p=−90P

D
Q=45 and P=-90P=−90

Answer 1

In order for the expression to have infinitely many solutions, we need to have a situation like this:

$Ax+B = Cx+D,\qquad A=C,\quad B=D$

In other words, we need the left and right hand sides to be the same, so that the equality is actually an identity, and no matter which x-value you choose, the equality will hold.

In your case, if you mimic the template above, you have

$A=-90,\ B = Q,\ C = P,\ D = 45$

And since we want $A=C, B=D$, we want

$P=-90,\quad Q=45$