Question

31. Rezolvaţi în mulţimea numerelor raționale ecuațiile: a) 2x + 7 - 3(x + 4) = - 4x -2(3-X); b) 4x + 7 + 5(x + 3) = 6x +1 ; c) 4(x + 3) - 2x = 6 - 3(2-x); d) 3(x-2) + 2x - 4 = 4(x + 1) + 6; e) 3(x - 5) + 5x - 7 = 5(x + 2) + 1; f) 5(x + 4) - 3x + 1 = 6(x + 3) -9; g) 5(x-3) + 4x - 6 = 4(x + 3) - 3; h) 7(x + 2) + 3x + 6 = 4(x + 5) - 18; i) 8(x + 2) - 2x + 4 = 3(x + 9) - 13 ; 1) 9(x - 2) - 5x + 7 = 4(x - 3) + 1​

Answer 1

a) 2x+7-3(x+4) = -4x-2(3-x)

2x+7 - 3x-12 = -4x-6+2x

x = -1

b) 4x+7+5(x+3) = 6x+1

4x+7+5x+15 = 6x+1

3x = -21

x = (-21):3 = -7

c) 4(x+3) -2x = 6-3(2-x)

4x+12 - 2x = 6 -6 + 3x

-x = -12

x = 12

d) 3(x-2)+2x-4 = 4(x+1) + 6

3x-6+2x-4 = 4x+4 +6

x = 20

e) 3(x-5)+5x -7 = 5(x+2) +1

3x-15+5x-7 = 5x+10+1

3x = 33

x = 33:3 = 11

f) 5(x+4)-3x+1 = 6(x+3) -9

5x+20 -3x+1 = 6x+18-9

-4x = -12

x = (-12):(-4) = 3

g) 5(x-3)+4x-6 = 4(x+3)-3

5x-15 +4x-6 = 4x+12 -3

5x = 30

x = 30:5 = 6

h) 7(x+2)+3x+6 = 4(x+5)-18

7x+14+3x+6 = 4x+20-18

6x = -18

x = (-18):6 = -3

i) 8(x+2)-2x+4 = 3(x+9)-13

8x+16-2x+4 = 3x+27-13

3x = -6

x = (-6):3 = -2

j) 9(x-2)-5x+7 = 4(x-3)+1

9x-18-5x+7 = 4x-12+1

4x-11 = 4x-11

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