To solve each compound inequality, we can break it into two separate inequalities and solve each one separately.
For the first compound inequality, f-4<5 and f-4 ≥ 2, we can break it into two separate inequalities: f-4<5 and f-4>2. Solving these inequalities separately, we get:
f-4<5
f<9
f-4>2
f>6
Therefore, the solution to the compound inequality is 6<f<9.
For the second compound inequality, y-1 ≥7 or y+3<-1, we can break it into two separate inequalities: y-1>=7 and y+3<-1. Solving these inequalities separately, we get:
y-1>=7
y>=8
y+3<-1
y<-4
Therefore, the solution to the compound inequality is y<-4 or y>=8.
For the third compound inequality, -5<3p+7≤22, we can break it into two separate inequalities: -5<3p+7 and 3p+7≤22. Solving these inequalities separately, we get:
-5<3p+7
3p>-12
p>-4
3p+7≤22
3p≤15
p≤5
Therefore, the solution to the compound inequality is -4<p≤5.