The solution set is $[0, \infty) $.
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+1)+2 \geq 3x+6\qquad $ ... distribute, simplify $4x+4+2 \geq 3x+6$ $ 4x+6 \geq 3x+6\qquad $ ... $/-6-3x $ $ x \geq 0$ The solution set is $[0, \infty) $.