Question

Find values for p and q so that x=5 is the only solution to the equation.
px–6=4(x+q)

Answer 1

Values of p and q are found by substituting x=5 into the equation px – 6 = 4(x + q), resulting in p=4 and q=-½ to ensure x=5 is the only solution.

Step-by-step explanation:

To find the values for p and q so that x=5 is the only solution to the equation px – 6 = 4(x + q), we can substitute x=5 into the equation and solve for p and q. After substituting x=5, we get p(5) – 6 = 4(5 + q), which simplifies to 5p – 6 = 20 + 4q. To have x=5 as the only solution, we need the coefficients of x on both sides of the equation to be equal (meaning p should equal 4) and the constants on both sides to also be equal. This gives us two equations:

1. p = 4
2. 5p – 6 = 20 + 4q, substituting p=4 gives us 20 – 6 = 20 + 4q, which simplifies to q = -½.

Hence, the values of p and q are 4 and -½ respectively, ensuring that x=5 is the only solution to the original equation.