Answer
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).
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$-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 $(-\infty, -4)$ .
