Answer:
Option b
[tex]p = -6[/tex] or [tex]p = 12[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the equation:
[tex]|p-3| = 9[/tex] has two cases
[tex](p-3) = 9[/tex] if [tex]h > 3[/tex] (i)
[tex]-(p-3) = 9[/tex] if [tex]h < 3[/tex] (ii)
We solve the case (i)
[tex]p = 9 + 3\\p = 12[/tex]
We solve the case (ii)
[tex]-p +3 = 9\\p = 3-9\\p = -6[/tex]
Then the solution is:
[tex]p = -6[/tex] or [tex]p = 12[/tex]
