Question

rezilvati in multimea Z* în ecuațiile:
| 2x-7 | < 9
2 x | 2x + 3 | -9 < 5​

Answer 1

Răspuns:

Explicație pas cu pas:

| 2x-7 | < 9

-9 < 2x - 7 < 9

-2 < 2x < 16

-1 < x < 8

x = {0, 1, 2, 3, 4, 5, 6, 7}

_____________

2*I2x + 3I - 9 :< 5

2*I2x + 3I < 14

I2x + 3I < 7

-7 < 2x + 3 < 7

-10 < 2x < 4

-5 < x < 2

x = {-4, -3, -2, -1, 0, 1}

Answer 2

$\it |2x-7|<9 \Rightarrow -9<2x-7<9|_{+7} \Rightarrow -2<2x<16|_{:2} \Rightarrow -1<x<8\ \ \ \ (1)\\ \\ x\in\mathbb{Z}^*\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow x\in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5,\ \ 6,\ \ 7\}$