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\begin{align} 3 \leq 2 x+2 < 6 \\ 1 \leq 2 x < 4 & \qquad \qquad \text{Isolate the variable term, and subtract 2 from all three parts.} \\ \frac{1}{2} \leq x < 2 & \qquad \qquad \text{Divide through all three parts by 2}.\end{align}