0
$\begingroup$

I'm having the most stupid of problems. Suppose I have a simple inequality like $$ |2-x|>2.$$

The solution to this is

$$ x<0 , \,x>4.$$

This is pretty obvious, though Mathematica insists on spitting back the input:

Reduce[Abs[2 - x] > 2]

outputs

Abs[2 - x] > 2

How can I tell Mathematica I want a series of expression with only $x$ on the LHS? Trying to solve for $x$ only makes Mathematica complain that the solution is full-dimensional, I assume this means that Solve can only output single points and not intervals. I also suspect this has to do with the fact that Mathematica doesn't really know $x$ is real, but

FullSimplify[Reduce[Abs[2-x] > 2], Assumptions -> x \[Element] Reals]

produces the same result.

$\endgroup$
7
$\begingroup$

Try

Reduce[Abs[2 - x] > 2, x, Reals]
(*x < 0 || x > 4*)
$\endgroup$
2
  • $\begingroup$ Well that was easy. Thanks, exactly what I needed. I'll accept when the 10 minutes pass. $\endgroup$ Dec 8 '20 at 12:57
  • $\begingroup$ Thanks, you're welcome $\endgroup$ Dec 8 '20 at 14:46
4
$\begingroup$

I always avoid using Abs since it is a Complex Function. Here we use RealAbs

Reduce[RealAbs[2 - x] > 2]
$\endgroup$
1
  • 1
    $\begingroup$ Also, Reduce[Sqrt[(2-x)^2] > 2, x] $\endgroup$
    – Bob Hanlon
    Dec 8 '20 at 15:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.