Question

2. Rezolvaţi în mulțimea numerelor întregi ecuațiile:
a) 23-3(4-5x) = 41;
c) 2(4x-13)-3(x+3)+13=2(2x
d) 2(3x+5)-5(1-2x) = 7(2x-3) + 18.
b) 15+7x-2(x-5) = 6(2x+5)-26; + 7)-29;​

Answer 1

a) 23 - 3(4 - 5x) = 41

23 - 12 + 15x = 41

15x = 41 - 23 + 12

15x = 30

x = 30 : 15

x = 2, solutie valida, ∈ Z

b) 15 + 7x - 2(x - 5) = 6(2x + 5) - 26

15 + 7x - 2x + 10 = 12x + 30 - 26

25 + 5x = 12x + 4

25 - 4 = 12x - 5x

21 = 7x

x = 21 : 7

x = 3, solutie valida, ∈ Z

c) 2(4x - 13) - 3(x + 3) + 13 = 2(2x + 7) - 29

8x - 26 - 3x - 9 + 13 = 4x + 14 - 29

5x - 22 = 4x - 15

5x - 4x = 22 - 15

x = 7, solutie valida, ∈ Z

d) 2(3x + 5) - 5(1 - 2x) = 7(2x - 3) + 18

6x + 10 - 5 + 10x = 14x - 21 + 18

16x + 5 = 14x - 3

16x - 14x = - 3 - 5

2x = - 8

x = -8 : 2

x = - 4, solutie valida, ∈ Z