Question

Rezolvați inecuația :
3(x+5)+2*|3x-1|+2x-7<5(x+1)+9,x∈N

Answer 1

3x + 15 + 2*|3x + 1| + 2x - 7 < 5x + 5 + 9 
2*|3x + 1| < 5x - 3x - 2x + 14 - 15 + 7
2*|3x + 1| < 6
|3x + 1| < 6/2
|3x +1| < 3
-3 < 3x + 1 < 3 / -1
-3 - 1 < 3x < 3 -1 
-4 < 3x < 2 / :3
-4/3 < x < 2/3
=> x ∈ ( - 4/3 , 2/3 ) , dar cum x ∈ N avem doar solutia 0.

Answer 2

3(x+5)+2*|3x-1|+2x-7<5(x+1)+9
x∈N=> x>0=> |3x-1|=3x-1

2*|3x-1|+3x+15+2x-7<5x+5+9
2*|3x-1|+5x+8<5x+14
2*|3x-1|<6
|3x-1|<3

-3 < 3x + 1 < 3 / -1
-4 < 3x < 2 / :3
-4/3 < x < 2/3
=> x ∈ ( - 4/3 , 2/3 )
x natural 
=> S=0