Answer
The solution set is $[2,\infty)$.
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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$ 5(3-x)\leq 3x-1\qquad $ ... distribute, simplify
$ 15-5x\leq 3x-1\qquad $ ... $/+3x-15$
$-8x\leq-16 \qquad $ ... $/\div(-8) \quad $ (negative!)
$ x\geq 2$
The solution set is $[2,\infty)$.
