Answer:
[tex]\huge\boxed{2<x<4\to x\in(2;\ 4)}[/tex]
Step-by-step explanation:
[tex]4<\dfrac{3x}{2}+1<7\qquad|\text{subtract 1 from all sides}\\\\4-1<\dfrac{3x}{2}+1-1<7-1\\\\3<\dfrac{3x}{2}<6\qquad|\text{multiply all sides by 2}\\\\(2)(3)<2\!\!\!\!\diagup\cdot\dfrac{3x}{2\!\!\!\!\diagup}<(2)(6)\\\\6<3x<12\qquad|\text{divide all sides by 3}\\\\\dfrac{6}{3}<\dfrac{3x}{3}<\dfrac{12}{3}\\\\2<x<4[/tex]
