The solution set is $(-\infty, -4)$.
Work Step by Step
The idea is to isolate x on one side. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $-4(x+2) \gt 3x+20\qquad $ ... distribute, simplify $-4x-8 \gt 3x+20\qquad $ ... $/-3x+8$ $-7x \gt 28 \qquad $ ... $/\div(-7) \quad $ (negative) $ x \lt -4$ The solution set is $(-\infty, -4)$ .