First, subtract #color(red)(6)# from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:
#abs(p + 7) + 6 - color(red)(6) > 10 - color(red)(6)#
#abs(p + 7) + 0 > 4#
#abs(p + 7) > 4#
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
#-4 > p + 7 > 4#
Now, subtract #color(red)(7)# from each segment of the system of inequalities to solve for #p# while keeping the system balanced:
#-4 - color(red)(7) > p + 7 - color(red)(7) > 4 - color(red)(7)#
#-11 > p + 0 > -3#
#-11 > p > -3#
Or
#p < -11# and #p > -3#
Or, in interval notation:
#(-oo, -11)# and #(-3, +oo)#
