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Find the solution set \(S\) of the inequality:$$ 3x + 2 < -2x + 12 $$Express your answer in interval notation.\FieldAnswerStudent{1}{$$\begin{aligned} 3x + 2 &< -2x + 12 \\ 5x + 2 &< 12 \\ 5x &< 10 \\ x &< 2 \end{aligned}$$ So, \(S = (-\infty, 2)\)}