Final answer:
To have infinitely many solutions for the equation 10x + p = qx - 5, p must equal -5 and q must equal 10.
Step-by-step explanation:
To find values for p and q so that the equation 10x + p = qx – 5 has infinitely many solutions, we must make both sides of the equation identical. This condition implies that the coefficients of x must be equal on both sides, and the constants must be equal as well. Hence, to satisfy the conditions for infinite solutions, we set 10 equal to q and p equal to -5.
Therefore, the values of p and q are: