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 COMPLICATED*SIMPLIFICATIONS
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])

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