Answer:
We can solve for p by isolating it on one side of the inequality symbol. First, we'll subtract 7 from both sides:
55 - 7 < -12p
48 < -12p
Next, we'll divide both sides by -12. Since we're dividing by a negative number, we'll need to flip the direction of the inequality:
48/-12 > p
-4 > p
Therefore, p is greater than -4. Written in interval notation, this solution is p ∈ (-∞, -4).