Question

solutia inecuatiei 3(2|2x+3|-7)+13 < 34,x apartine Z*

Answer 1

3(...)<34-13=21

(...)<7

2|...|-7<7

2|...|<14

|...|<7

|2x+3|<7

-7<2x+3<7

-10<2x<4

-5<x<2

x∈(-5;2)∩Z={-4;-3;-2;-1;0;1}

Answer 2

$\it 3(2|2x+3|-7)+13<34|_{-13} \Rightarrow 3(2|2x+3|-7)<21|_{:3} \Rightarrow \\ \\ \Rightarrow 2|2x+3|-7 < 7|_{+7} \Rightarrow 2|2x+3| < 14|_{:2} \Rightarrow |2x+3| <7 \Rightarrow \\ \\ -7<2x+3<7|_{-3} \Rightarrow -10<2x<4|_{:2} \Rightarrow -5< x < 1 \ \ \ \ (*) \\ \\ x\in \mathbb{Z}^* \ \stackrel{(*)}{\Longrightarrow} \ S=\{-4,\ \ -3,\ \ -2,\ \ -1\}$