Question

Rezolvaţi în mulțimea numerelor întregi ecuațiile:
a 2(4x + 5) =-3x + 32;
b 3(-2x + 7) = -5x + 23;
c-3(-x + 1) = 3x - 3;
d -2(x – 4) + 6 =-4x + 5(x - 2);
e 5 - 3(x+2) = 2x + 3(x+5);
f 5+4(1 - x) = 3x +9. ​

Answer 1

a) 2 (4x + 5) = - 3x + 32

<=> 8x + 10 = - 3x + 32

<=> 8x + 3x = 32 - 10

<=> 11x = 22

<=> x = 2

b) 3 (- 2x + 7) = - 5x + 23

<=> - 6x + 21 = - 5x + 23

<=> 21 - 23 = - 5x + 6x

<=> x = - 2

c) - 3 (- x + 1) = 3x - 3

<=> 3x - 3 = 3x - 3

<=> x ∈ Z

d) - 2 (x – 4) + 6 = - 4x + 5 (x - 2)

<=> - 2x + 8 + 6 = - 4x + 5x - 10

<=> - 2x + 14 = x - 10

<=> 3x = 24

<=> x = 8

e) 5 - 3 (x + 2) = 2x + 3 (x + 5)

<=> 5 - 3x - 6 = 2x + 3x + 15

<=> - 1 - 3x = 5x + 15

<=> 8x = - 16

<=> x = - 2

f) 5 + 4 (1 - x) = 3x + 9

<=> 5 + 4 - 4x = 3x + 9

<=> 9 - 4x = 3x + 9

<=> 3x + 4x = 9 - 9

<=> 7x = 0

<=> x = 0

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Answer 2

Răspuns:

a. 2(4x + 5) =-3x + 32

8x+10=-3x+32

8x+3x=32-10

11x=22=>x=22:11=>x=2

b. 3(-2x + 7) = -5x + 23

-6x+21=-5x+23

-6x+5x=23-21

-x=2=>x= -2

c. -3(-x + 1) = 3x - 3

3x-3=3x-3

3x-3x=-3+3

0=0

d. -2(x – 4) + 6 =-4x + 5(x - 2)

-2x+8+6=-4x+5x-10

-2x+4x-5x=-10-14

-3x=-24=>x=24:3=>x=8

e. 5 - 3(x+2) = 2x + 3(x+5)

5-3x-6=2x+3x+15

-3x-5x=15-5+6

-8x=16=>x=-16:8=>x= -2

f.  5+4(1 - x) = 3x +9

5+4-4x=3x+9

-4x-3x=9-9

x=0