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