Question

Rezolva ecuațiile in z a) 5x-45=7x+33 b) |5x+4|=11

Answer 1

Răspuns

Explicație pas cu pas:

Z={...,-3,-2,-1, 0, +1,+2,+3...}

a)

5x-45=7x+33

5x - 7x = 33 + 45

- 2x = 78

x = 78 : (-2)

x = - 39

b)

|5x+4|=11

5x + 4 = 11                   5x + 4 = -11

5x = 11 - 4                    5x = - 11 - 4

5x = 7                          5x = - 15

x = 7 : 5                       x = - 15 : 5

x = 1,4                          x = - 3

S = { - 3}

Answer 2

$\it x\in\mathbb{Z}\\ \\ a)\ 5x-45=7x+33 \Rightarrow -45-33=7x- 5x\Rightarrow -78=2x \Rightarrow \\ \\ \Rightarrow 2x=-78 \Rightarrow x=-78:2 \Rightarrow x = -39\in\mathbb{Z}\\ \\ b)\ |5x-4|=11 \Rightarrow 5x-4=\pm11 \Rightarrow 5x-4\in\{-11,\ 11\}|_{+4} \Rightarrow \\ \\ \Rightarrow 5x\in\{-7,\ 15\} \ \ \ \ (1)$

$\it x\in\mathbb{Z} \Rightarrow 5x\in\mathbb{Z} \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 5x=15 \Rightarrow x=3\in\mathbb{Z}$