Question

Which values of P and Q result in an equation with exactly one solution? 2x+Q=Px−31 Choose all answers that apply: Choose all answers that apply: A -Q=−31 and P=−2 B- Q=31 andP=2 C - Q=−31 and P=2 D - Q=-2Q=−2 and P=2

Answer 1

Option A is correct

Values of P = -2 and Q = -31

Explanation:

Given the equation:
`2x+Q= Px-31`

Now, we put the given values

A.

Q = -31 and P = -2

2x + (-31) = -2x - 31

2x - 31 = -2x -31

4x = -31 + 31

4x = 0

x = 0 [one solution]

B.

Q = 31 and P = 2

2x + Q = Px -31

2x + 31 = 2x -31

Subtract 2x from both sides we get

31 = -31 False.

C.

Q = -31 and P = 2

2x + (-31) = 2x - 31

2x - 31 = 2x - 31 [More than one solutions, for any x]

D.

Q = -2 and P = 2

2x + Q = Px -31

2x + (-2) = 2x -31

2x -2 = 2x -31

2x - 2x = -31 + 2

Combine like term;

0 = -29 False.

Therefore, the values of P and Q results in an equation with exactly one solution is; P = -2 and Q = -31