Question

4. Rezolvați în mulţimea Z* inecuațiile:
a) |2x -7|<9
b) 2|2x + 3| - 9 < 5​

Answer 1

b)

$\it 2|2x+3|-9 < 5\Big|_{+9} \Rightarrow 2|2x+3| < 14\Big|_{:2} \Rightarrow |2x+3| < 7 \Rightarrow \\ \\ \\ \Rightarrow -7 < 2x+3 < 7\Big|_{-3} \Rightarrow -10 < 2x < 4\Big|_{:2} \Rightarrow -5 < x < 2 \Rightarrow \\ \\ \\ \stackrel{x\in\mathbb{Z}^*}{\Longrightarrow} x\in\{-4,\ -3,\ -2,\ -1,\ 1 \}$