Question

Which values of P and Q result in an equation with no solutions?

Px - 45= Qx+75

A. P=-45 and Q=-75
B. P=45 and Q=-15
C. P=15 and Q=15
D. P=15 and Q=75

Answer 1

Px - 45 = QX + 75

Px - Qx = 75 + 45 = 120

A. If P = - 45 and Q = - 75, then

- 45x + 75 x = 120

30x = 120 and x = 40

B. If P = 45 and Q = - 15, then

45x - 15x = 120

30x = 120

x = 40

D. If P = 15 and Q = 75, then

15x - 75x = 120

- 60x = 120

x = - 2

C. If P = 15 and Q = 15, then

15x - 15x = 120

0 = 120 which is absurd.

Hence, P = 15 and Q = 15 result in an equation with no solution.