Question

find values for p and q so that x = -2 is the only solution to the equation.
px + 2 = 4x + q
p =
q =

Explanation:

Step1: Substitute \( x = -2 \) into the equation

Substitute \( x = -2 \) into \( px + 2 = 4x + q \), we get \( p(-2) + 2 = 4(-2) + q \), which simplifies to \( -2p + 2 = -8 + q \).

Step2: Analyze the equation for only solution

For the equation \( px + 2 = 4x + q \) to have only \( x = -2 \) as a solution, the coefficients of \( x \) must be equal (so that it's not a contradiction or an identity with infinite solutions), so \( p = 4 \).

Step3: Find \( q \) when \( p = 4 \)

Substitute \( p = 4 \) into \( -2p + 2 = -8 + q \), we have \( -2(4) + 2 = -8 + q \). Calculate the left side: \( -8 + 2 = -6 \). So \( -6 = -8 + q \). Add 8 to both sides: \( q = -6 + 8 = 2 \).

Answer:

\( p = 4 \)
\( q = 2 \)