Question

Write each of the following sets as intervals :
1. {x belongs to R : 1 > 2x - 3 > 0 }
2. {x belongs to R : 3/2 < 2 + 3x < 5 }

Answer 1

$$\begin{gathered} 1) \\ 1\ge 2x-3\ge 0 \\ 4\ge 2x\ge 3 \\ 2\ge x\ge \frac{3}{2} \\ Sox\in \left[\frac{3}{2},2\right] \\ 2) \\ \frac{3}{2}<2+3x<5 \\ \frac{3}{2}-2<3x<5-2 \\ -\frac{1}{6}<x<1 \\ x\in \left(-\frac{1}{6},1\right) \end{gathered}$$