Question

What solution value satisfies the compound inequality 4 < 3x∕2 + 1 < 7?

Answer 1

Answer:2<x<4

Explanation:

Answer 2

`\huge\boxed{2<x<4\to x\in(2;\ 4)}`

Explanation:

`4<(3x)/(2)+1<7\qquad|\text{subtract 1 from all sides}\\\\4-1<(3x)/(2)+1-1<7-1\\\\3<(3x)/(2)<6\qquad|\text{multiply all sides by 2}\\\\(2)(3)<2\!\!\!\!\diagup\cdot(3x)/(2\!\!\!\!\diagup)<(2)(6)\\\\6<3x<12\qquad|\text{divide all sides by 3}\\\\(6)/(3)<(3x)/(3)<(12)/(3)\\\\2<x<4`