solve limitations

[Damiano Pasetto]

Hi,

I am quite new to SageMath. I wanted to use Sage to solve some easy equations and inequalities, but frequently the solve command doesn't provide any answer, sometimes the answers should be simplified, and sometimes it even gives wrong answers.

Am I doing something wrong? 

If sage cannot solve those simple problems, how can it be a valuable alternative to mathematica?

I am copying here some examples:

1) NOT SOLVIG

in: solve(abs(x-4)==x,x)

out: [x == abs(x - 4)]    NOT SOLVIG

(correct: x=2)

2) WRONG ANSWER

in: solve(abs(x+1)>=x,x)

out: [[x == 0], [0 < x], [x < 0]]   WRONG

(correct: all values of R)

3) NOT SOLVING

in: solve(x^2+abs(x+1)==4,x)

out: [x == -sqrt(-abs(x + 1) + 4), x == sqrt(-abs(x + 1) + 4)]    NOT SOLVIG

(correct: [(-1+sqrt(13))/2, (1-sqrt(21))/2])

4) CORRECT ANSWER BUT COMPLICATEDSIMPLIFICATIONS

in: solve(abs(5*x-1)>=x,x)

out: [[x == (1/4)], [x == (1/6)], [x == 0], [0 < x, x < (1/6)], [(1/4) < x], [x < 0]]    TOO COMLICATED

(correct: [x<=(1/6)], [x>=1/4])