Answer
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).
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$ 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 $[6,\infty)$.
